I won't repeat the already existing, good, answers, but here are a few other options.
Let them forget they're fighting you
If a toddler has it in their mind to be contrary it's hard to get anything done with them; but luckily toddler's forget what they're doing pretty quickly. Sometimes just leaving the subject alone for a minute, while distracting them with something else, will give enough time for the toddler to forget that they were resisting you. Then you can ask them again to do something in a few minutes they may do it without complaint this time, not remembering they had intended to fight you on it.
To give an example of this I remember one time when my goddaughter was very tired but actively fighting any attempt to sleep she would run away crying if I so much as tried to pick her up (knowing I would try to put her to sleep). I let her wander away crying in anger for a few minutes. When I didn't follow as she expected and allowed her half a minute of alone time she instead became upset that she was now alone in a dark house without anyone to comfort her when upset and came back to me, still crying, but now wanting me to pick her up to comfort her; she fell asleep in my arms shortly after. Had I continued to follow her and try to pick her up that stubborn child would have resisted me for another half an hour at least most likely, letting her alone for a minute was enough time for her to flip from actively resisting me to desperately wanting my comfort.
Give them choices, that both result in what you want.
Even a toddler wants to feel like they have control of their life, and are more likely to work with you when they feel they have it; so let them make choices. Give them lots of choices to pick from, just make sure all the ones you suggest happen to be choices that move you forward towards your goal.
If the child won't get dressed ask them which panties they want to wear or if they want a dress or to wear their new shirt this morning. If you preempt resistance by getting them involved in deciding what they will do they likely cooperate more. Once a child picks an article of clothing they like they usually put it on without complaint because it's their clothing now.
Concede without actually conceding
Sometimes it helps to let your child think they won a battle, without giving up anything you really care about. If the kid is adamant that they don't want to wear shoes give up and let them wear their rain boots. If they insist that they don't want to be carried by you ask if they would like a piggy back ride or to ride on your shoulders. Basically this is similar to the above idea of giving different options that all lead to what you want, but done only after they resist instead of preempting them with choices.
You don't want to give in too often or you teach a child that if they resist they get other things of course. My general rule is if a child is resisting 'nicely', ie without screaming, throwing tantrums, or being too disruptive then they can bargin to get other options, but if they throw tantrums or cause too much trouble they loose the right to get alternatives like this offered to them, to teach them the importance of being civil even in disagreement without encouraging any of the really nasty behaviors.
Long term vs short term approaches
As a sort of aside when dealing with kids I find myself often in a situation of deciding which approach I want to use to deal with a child that refuses to cooperate, the short term or the long term. The short term approach is the one that gets a child to do what you want right now. That includes things like distraction, making games out of the activity, and most of the things suggested by the other answers. These are good options and I use them all the time, but all of them are things that work to solve the current situation only, and not necessarily work to train a kid to cooperate with you more in the long term.
Most of the stuff below this point tend to fall a bit more on the 'long term solution' scale of things, as their things that take a bit longer and are general intended to work towards teaching a child that generally when they listen to you and cooperate they have fun, and when they resist and fight they tend to have less fun; thus the best thing to do is to not fight.
Both long and short term solutions are valuable techniques to have in your 'repertoire'. There are many times when you can't afford the extra time and effort to try a long term solution, and preempting potential resistance by offering choices or making a game out of an otherwise disliked activity will allow you to spend more time having fun with a child rather then fighting them. Still, your going to need to use some more long-term tricks to teach your child the importance of behaving well at some point.
When a child I'm caring for or mentoring is misbehaving I often find myself asking an important question, is this situation one where I need to get them to cooperate now, or is it one I can use as a teaching experience. Sometimes I'm in a rush and just want to do anything (short of encouraging bad behaviors) to get the job done. Sometimes I'm not in a rush, or see a particularly good opportunity to teach the child, and then I will fall back on the more long term teaching experiences. I use both tricks, you don't always have to fall back on doing it the hard way, so long as occasionally you fall back on the slower teaching opportunities to reinforce good lessons.
Utilize natural consequences to reinforce rewards and punishments
I understand your seemed to rule out reward and punishment, to encourage behavior, but there are some methods that make these technique more effective, and one of them is to make sure the consequences feel a natural result of their actions.
So for example a punishment for not putting on their clothes in the morning may not be that you take away desert; those are unrelated in their mind. Instead let them get ready slow and miss their opportunity to go to the park/on a playdate/on a fun adventure which was planned. Here the cause and effect are direct, I took too long and so It was too late to do what I wanted to do. It makes consequences a little more likely to work.
This works even better with rewards. I understand your not wanting to teach a child they get a reward every time they do a task you want; but if the reward is a natural consequence of doing the thing you want them to do then you can tempt them with the reward without risking teaching the child that they should get rewarded every time they listen.
For instance if a child is slow to eat you can remind them that you have their favorite fruit, or even a donut, for breakfast; but you can't eat until you finish getting dressed. Here your still effectively tempting them with a tasty treat to speed up their getting dressed; but your not telling them it's a reward for getting dressed. by presenting it this way your not teaching them that they deserve, and should thus demand, a donut every time they get dressed because the donut isn't actually contingent on their getting dressed. Instead what they are hearing is that this morning your already planning to give them something they happen to want, and that the thing delaying that outcome is their own resistance.
Make resisting be boring
This is partially just a specific example of natural consequences, but try to arrange that the natural consequences of resisting are not fun. For example they can resist getting dressed, but until they do your not opening the door to their room so their stuck in their room and missing out on playing with toys/watching tv/etc they may do elsewhere. Or your not starting the next game they want to play until they help pick up the toys from the current game they just finished etc. try to present things in a way that leads to the 'natural consequences' of resisting being stuck without anything fun to do.
An important part of this though is realizing sometimes resisting is the fun for the child. I had one child in Sunday school I use to assist in who would always get up and run out of the room because he knew someone would have to chase him to catch him, and to him that was fun. He wanted attention and he got it when he misbehaved. To encourage him to act the way we wanted I had to figure out a way to 'punish' him that involved giving him as little attention as possible (while still keeping him from being a distraction to the rest of the class). In this case it meant staying near him to catch him whenever he tried to run away, but while explicitly not answering questions, talking, or interacting with him in any other way, combined with giving him far more attention when he was behaving and not trying to get away so that he learned the way to get the attention he wanted was by listening, not by forcing me to chase him.
Similarly sometimes if a child is throwing a temper tantrum the best thing to do is let them alone with their temper tantrum. It's not fun to cry, or sit in a corner pouting. Sometimes letting them miss out in fun because of their own insistence on fighting you is the best approach. Instead of continuing to fight them when stubborn just let them make themselves upset, is a far more effective punishment then you could inflict for misbehaving.
Ff you do this make sure you make it clear to the child that you are not going to give in or cooperate with the tantrum, but that you are available at any time to help or comfort them as soon as they decide they want it! The lesson your trying to teach is not that you gave up on them and don't care that their crying/upset after all; instead your trying to teach them that you are always there and want to comfort them, but they are the ones preventing you from doing it by having their temper tantrum. Their fighting is preventing you from comforting them and making things better.
As a common example I may allow a child who is acting stumborn or upset to walk away to show that they are angry at me. I won't follow them, but I will tell them that I love them and as soon as they are ready I'm here to help/play/comfort them (depending on what originally triggered the fight). I'll leave them mostly alone, not rewarding their tantrum with allot of attention or giving them the impression that I'm being hurt by their tantrum (as this is often the whole point of the tantrum). I will, however, occasionally remind the child that I love them and "when you are ready" I'm still here. After that I just wait the child out until they realize that their not going to win anything with their tantrum and they child decides to come back and reingage me because they are not enjoying the lost fight and are missing out on all the fun things we can be doing. When the child comes back I'll again remind them that I love them and tell them I'm glad they are ready to talk/play/clean-up etc.
Of course this just a very specific example of a more general approach
Use yourself as the reward you offer a child, and removal of you as a punishment
You are something your child values! Your one of their most consistent playmantes, one of their key sources of comfort, and the one who provides them with most of their needs. Even when they are fighting you they value you; which in turn that your presence, and interaction, with them can be both a reward for good behavior and serve as something to take away as a punishment for bad behavior, though the latter needs to be done carefully to communicate the right lession.
Lets start with the safer example of using yourself as a reward. One on one time and active playing with your child is something they should value, and thus can be offered as a reward for good behavior. If they will clean up this mess then your play that favorite game they like with them, or if they share that toy they don't want to share your reward them by doing something even more fun with them like tickling them or spinning them in circles etc. Note this should be additional quality fun with you, above and beyond what they usually get. Obviously they should already be getting love and attention from you throughout the day, they shouldn't be expected to 'earn' every interaction with you, but more interactions will always be welcome.
As you mentioned the downside of using rewards to encourage behavior is to monitize something, teaching a child that they should only do some good behavior if they receive the appropriate reward. However, when your reward to a child behaving is more quality interaction what your teaching the child is "behaving in a good way encourages others to want to spend time with you and do things with you", which is essentially the whole reason we want the kid to learn to behave in the first place, so it hardly seems a negative lesson to be teaching the child.
On the other side of things you can remove yourself from a situation if a child is misbehaving as a sort of punishment, though again this should be done carefully so as not to teach the child that you don't love them if the misbehave. Instead I usually work removing myself from a child into natural consequences, by explaining how/why their action is preventing me from interacting with them. something like "I love to play with you, but I don't like it when you play so rough with me. I'd like to play with you as soon as your ready to stop playing so rough".
In every case when I remove myself from a child I'm not isolating them entirely. I always reiterate that I love them even as I'm distancing myself from their behavior. I always stress that I want to do something with them, and explain how/why their action is making it hard for me to do that thing with them. Thus the message is not that I've stopped caring for them, but that while I still care for them they are preventing us from having fun I'd like to have with them because of their negative actions.
Again, this is an option that can be effective but shouldn't be over-used, as you don't want to teach a child that your affection is entirely conditional on good behavior. One of the reasons I decided to list it is that it's particularly effective for me when volunteering with children. As a volunteer who isn't a parent I can't force a child to sit in time out if they resist (I don't want to be man handling someone else child), nor can I take away a toy if they disobey etc. One of the few forms of 'punishment' for misbehaving I can always utilize when volunteering is removing myself from play. Thus I've used this far more with kids I'm volunteering with when I can't resort to other forms of punishment/reward then I did with my own kids.
Be consistent, and don't say something you don't mean!
Of course this is always a true statement, but when it comes to punishment, or reward, one of the most important things is to be consistent. If you threaten a punishment and don't follow through the child will very quickly learn that your threats mean nothing, and stop paying attention to them. Never make a threat you are not willing to follow through with, or promise a reward your not certain you can provide!
Don't hesitate to use random surprise rewards
You don't want to teach a child that they should expect to get a reward every time they do something, but you do want to show a child that certain actions are deserving of being repeated, and one way to do this is surprise rewards.
Instead of giving a child a reward every time they behave, reward them only occasionally, after they already did something positive, and explain it's because of their good behavior. Because the reward is coming later, not as part of a condition of their doing the good behavior, and because it's random enough that they never learn to expect/demand a reward for doing the good behavior, your not teaching them that the behavior should only be done for a reward; but you are encouraging them to keep up the behavior you like.
I try to look for any situation when a child does particularly noteworthy or above and beyond my basic expectations, or when a child tolerates a negative experience without complaint when I would have expected more resistance; but in general I'm always looking for opportunities to reward a child for good behavior.
Those rewards can be as simple as praising them for doing something well. Praise is a surprisingly effective reward, but I'll sometimes include a more material reward like a piece of candy or getting to stay up a little later then usual. The most common reward is getting to do something they enjoy with me. For instance I save favorite games that are particularity taxing on me (such as spinning them in the air or letting a larger kid ride on my shoulders after their getting to big to do long rides without tiring my shoulders) as rewards for when I see them do something positive.