I completely relate - know that it gets better. When my little girl was four she went through a phase almost exactly like the one you describe - except instead of tantrums she dissolved into tears.
First, you should know that developmentally a lot of things are going on at four and they are growing in ways that are much more difficult to "see" than when they are just a bit younger. They begin to realize there can be different perceptions and different knowledge about things between people (a precursor in understanding required for integrating an understanding of "real" and "fiction", for the ability to lie in order to deceive, and in fully relating with others in imaginative and collaborative play). I'd imagine there is a certain amount of anxiety that comes with this as they start to understand they can't just trust every one they meet the way they once did. There is also a lot of growth in the frontal cortex which can make things confusing and stressful too. For more information on the toddler-preschool brain (the article talks about kids aged around 3) and how that plays a part in tantrums click here (parenting magazine).
They are also moving steadily toward more independence and they stop looking so "babyish" and start really looking like "kids." Without even realizing it, the adults around her start to expect a lot more of her (and she is mostly ready for those expectations). Many four-year-olds get a bit "clingy" or "needy" in various ways. Kids that a month ago had the ability to tie shoes for themselves will suddenly "forget" and want help, or (at the preschool) kids that previously had no difficulty when they got dropped off, will need a little extra reassurance that mom will come back at the end of the day (seriously, even those that have attended preschool since they were barely two and whose mothers never forgot to come get them). I figure it is one way to cope with all these realizations.
It is a bit like when little ones start walking. With some kids you know they can walk, but they aren't ready to believe it so they still cling and hold on until one day the temptation to grab something over-takes them and they forget to hold on.
It sounds to me as though that is where your daughter is at the moment. Knowing that, you might want to make a point of spending a little extra time with the story part of the bedtime routine, incorporate asking her how her day was, what she did and learned etc. at some regular time and event like over dinner or on the car-ride home from school. Really make sure you add some extra quality time - just as a preventative measure.
What worked really well for us, was to say to our daughter, "I see you are upset, but crying won't help solve the problem. When you are ready to talk about it, let me know" Then we'd give her a soothing pat, brief hug or kiss and give her a little time to "recover." (btw, recovery took place in her room, or in a "quiet" place away from us). When the drama part was over she could come to us and we would guide her through her decision. "I want to help you hon, but I don't understand which clip it is you wanted. You'll just have to show me."
If we were in a hurry, we would say something more like, "I understand you are upset, but if you can't just go get the clip you want quickly, there just isn't enough time for me to do anything about it and you'll have to wear this one." Then, we let her be upset about it. It was her decision to wallow in her disappointment or to buck up and move on quickly and there-by actually get what she wanted. Either way, we administered without much emotion other than those emotions that expressed sympathy.
My husband had a particularly difficult time with this and often he would try to reason with her to calm her down. The more he said or did to calm her, the more upset she got. Then, he would get frustrated and yell, "Oh stop crying about it" or vent his frustration with her lack of reason in some fashion. This, of course, made the tearfulness get 100 times worse. It didn't take long before he realized that one-two quick sentences of support followed by a "It is your decision how quickly you move on" kind of attitude was rewarded with the quickest path to daughter drama recovery.
I would also suggest taking a look at some of the questions already asked about tantrums such as This Question or this question. The first one covers tantrums with a two year old, but may still have some good information. In particular, in the second one, I would look at Christine Gorden's Answer and see if it applies to your situation.
It did take about a month to get through the bulk of the phase, but in the grand scheme of things, it didn't take very long before she skipped all the drama and just went straight to the "problem solving" part. She still gets dramatic sometimes - especially if she is overtired or overstimulated, but we were mostly past it by the time she turned five (until, that is, the hormones start kicking in I suspect).