id definitely echo strengthdawg on bands teaching you how to use the muscle you have explosively, and that some people are just explosive to start with (usually people with better relative strength)
i have also found the same as fletch, if you let the bar get forward on you with heavy band tension that bar will be bouncing off the floor before you know it.
personally bands work for me on bench cos im pretty weak off the chest and my shoulders cant stand up to huge volume so a paused bench with bands lets me hit both. also for ballistic bench, awesome, cant emphasise enough how much of a difference this made to my bench. ive been doing heavy jump squats for a while but not until i got bands could i do the same thing safely with the bench. i also do the whole dynamic-kinetic-whateveryoucallit: hanging weights off the bar from bands. my shoulders are completely shot so they love me for doing anything that builds the stabilisers. come to think of it i dont know why ive never done this on a squat, ill have to try that.
for the squat i dont use them that much, usually when i go for a 5RM on ATG high bar squats, just because theyre brutal and feel great. sometimes on box squats, and almost always on heavy good mornings cos i dont like cutting the ROM but then its tough to overload the top.
a bit like GMs, i love bands for RDLs, or anything where you get a good stretch before an explosive, hard contraction. i do use them on conventional deads from time to time when i stop remembering to accelerate all the way through the lift (ive never done a reverse band dead, dunno why not).
more and more though i use bands for accessory work, a lot of the time on their own. right now im loving facepulls with just bands, also pullaparts, pullthroughs, flyes, whatever. plus you can do them anywhere, anytime, just grab a band and go.
oh, and one more, assisted chinups on the rings, my new wife's new favourite thing, she likes the bouncy motion...