We're going to take advantage of the fact that in the first few minutes in the slow cooker, the cup both softens and expands. This behavior can be manipulated by applying a constant force to some parts of the cup, making it collapse inwards instead.
Take a coffee cup, and put a rubber band around it near the top. Put it in the bowl, replace the lid, and boil for a couple of minutes (watch it, don't time it!). Remove once suitably shape-changed, and take off the rubber band. Done!
Try putting two bands on, or put an odd-shaped object inside to act as a mold (I ran out of used coffee cups, so haven't actually tried the latter). This project is great for experimentation to see what effects you can achieve.
Tip: get the rubber band as tight as possible. Strong, tight bands will create the most interesting effects.
COASTER19 advises that if you have a pressure cooker, you get best results from looser bands, with the cup upside down, and a 7-minute cooking time.
Valaynetine reports that some sorts of polystyrene cup don't change shape at all. The ones I tried - all the same sort - were a soft, relatively bendy type of cup, so that's probably the style to use.
calischs from InstructablesTV made a short video based on this instructable, and cut the rim off then immersed the cup in boiling water with the help of a metal weight. It seemed to work well. Check it out, it's only 46 seconds long!
rojo.balloon made a styrofoam hat from a bowl.
Maurice1985 made an instructable (and made lots more vases than me!) showing how you can fill these with concrete to make a more permanent vase.