Verbs:
* General: clean up, cheer up, dress up, give up, grow up, hang up, look up, make up, pick up, put up, show up, shut up, speak up, stand up, stay up, tear up, wake up, warm up, work up, write up
* Phrasal verbs: back up, break up, bring up, call up, catch up, come up, cut up, end up, figure out, find out, get up, give up, go up, hold up, keep up, look up, make up, mix up, move up, pick up, put up, run up, set up, shut up, speed up, take up, turn up, use up, wait up, wake up, work up, write up
* Idioms: beef up, brush up, come up with, end up, follow up, get up to, go up in smoke, keep up with, make up for, mess up, screw up, stand up for, step up, take up with, think up, work up to
Nouns:
* General: backup, checkup, cleanup, followup, makeup, setup, signup, startup
* Idioms: catch-up, follow-up, kick-up, makeup, screw-up, stand-up, wakeup
Adjectives:
* General: mixed-up, screwed-up, wrapped-up
Adverbs:
* General: back up, cleanup, follow up, makeup, setup, speed up, wakeup
Other:
* Phrases: all up, all wrapped up, at up, better up, big up, break up, catch up, clean up, come up with, end up, get up to, give up, go up, hang up, hold up, keep up, look up, make up, mix up, move up, pick up, put up, right up, run up, set up, show up, shut up, speed up, stand up for, step up, take up, tear up, think up, turn up, use up, wait up, wake up, warm up, work up, write up
This is not an exhaustive list, but it gives you a good starting point. Remember, you can also add "up" to many other words and phrases to create new expressions.