It's been a while since I've been camping and I never did so as a very young child. What types of activities and general camping prep would be appropriate for going with a kindergartner?
Where and how are you going camping? Woods survival style (no power etc)? Campsite at a local lake? Campsite at a state park? Someone's back 40?
For the sake of the answer, I'm going to assume that you're doing like most people and get a powered campsite near a local reservoir. So basically a mowed lawn bordered by non-mowed scrub vegetation bordered by maybe woods or untended land.
activities for a 5yo that are different from general daily activites: bubbles, airplanes, ball of any sort. (bocce is simple and fun for anyone that can hold a ball, excellent in grass or on a beach).
and then there's nature: sticks, rocks, turtles are fun at that age but need an element of care. the problem is that a lot of parents get so stuck on "OMG OMG OMG" that they forget that THEY used to sled down the hill at 40mph towards the 10' cliff that overlooked a creek . . . and lived to tell about it. you know what? your 5 yo will too. Let them get a walking stick and play in the mud. you're camping. who cares if they get covered. OH NO now you have to get in the water!
As far as prep, have plenty of Koolaid and snacks they like. get their fave blanket and plillow and 2ndary fave toys . . . something WILL get lost or left, and it'd best if it wasn't Bunnie.
Bottom line is this: they'll have just as much fun left to their own devices under your watchful eye as they would if you perseverated over every pixel of their activitiy in the name of safety. Don't forget that you're all there to have fun!
 OH OH I forgot... one year we went camping with a 5 and 3 yr old plus I guess 15 and 13 boys. There were probably >6 families and others. Total numbers something like 25-30 people. We made up a board game using the checkerboard pattern on a table cloth we bought, playing cards and a couple of dice. some kids pulled cards to move pieces (bottle caps, fingernail clippers, etc) while other kids were actors and had to act out "something" whenever either a face card was drawn or the player landed on a corner... in other words it happened a lot. If 2 players shared a space, their representative 'actors' had to do best-of-3 rock/paper/scissors... the guy that won moved ahead one space. The person that won got a twinkie... and yes we were all sitting there eating twinkies.
Etc. etc. etc. The point of this addon-edit is that board games are great, but making up your own games is even better. We played that game off-n-on the entire w'end. If there's a good number of people with a concentration of children (it was probably 50/50 for these campouts) then you can easily occupy several hours just chilling with your goofy game.
- hot chocolate
- board games
What a fun question. Take them for a hike, teach them to fish, try to capture fireflies, help them to make some scrammbled eggs, teach them to build a fire (with supervision), have them collect the sticks to make the fire. Tell them a story about the woods, have them tell you a story about the woods (kids can be creative when you let them). hide and seek is fun, build a damn, if possible. Play I spy, bring some books, play some cards, play yatzee, write a song, play fill in the blank, you make up a story and leave blanks in the story having them put words in, then read the story back to them. Collect crayfish, leaves or pine cones. Hide something near the campsite and let them look for it.
Do a photographic scavenger hunt, traveling journal, and an upside down hike (make sure to take a magnifying lens). All of these activities are outlined on my website for details about "how to"
You can also make "Hobo Stew" (In the morning get a fire roaring and wrap potatoes in foil. Peel the foil open a little and slit open the potato. Now, allow your kids to add from a selction of pre-chopped veggies into the middle of the potato add canned beef stew to each and seal back up. Reduce the fire and place the foil packets into the hot coals. Allow to roast and eat.), and roast hot dogs and marshmallows (just teach them fire safety first)
First learn about staying away from poison ivy, nettles and other "dangerous plants" in the area where you will be and then do a leaf or flower collection with a plant press.
Wake up for the "Morning Chorus". Wake up before sunrise and hike to a field or meadow away from other campers. Sit and get cozy (bring blankets) and sit very still and quiet as the sun rises. If you are quiet enough you'll get to hear the cacaphony of all the birds calling out their territories to each-other. You'll see lots of the birds too so bring along a peterson's field guide to birds for your area as well as the blankets and water to drink.
If you'll be at a national park look up their "Junior Ranger Program" and they will have a packet of activities related to the specific park for your kids to choose amongst. When they have completed a certain number they can show what they've done to a ranger adn get a patch. It is a pretty cool program and most of the parks I've been to have pretty good activities with a range of levels so there is always something age-appropriate.
Volunteer. Perhaps there is an invasive plant species that needs eradicating and you can spend part of a day helping with a group working in an area particularly effected. Or perhaps they need a clean up crew and will give you tools to safely gather a bag of trash at your location.