General:
* Crush
* Wrinkle
* Scrunch
* Compress
* Bend
* Fold
* Crease
* Mash
* Squash
* Collapse
For paper or fabric:
* Scrunch up
* Ball up
* Roll up
* Flatten
* Wrinkle
* Crease
For something solid:
* Collapse
* Cave in
* Buckle
* Yield
* Give way
* Dent
* Distort
Figuratively:
* Break down
* Fall apart
* Wither
* Decline
* Subside
* Give in
The best synonym for "crumple" will depend on the specific context in which you are using it. For example, if you are talking about a piece of paper, "scrunch up" might be a more appropriate synonym than "collapse."