Render Files - nothing is dependent on these, except playback. Be sure to go into Preferences and turn Background Rendering the heck OFF! Delete these regularly, you can easily regenerate them when needed.
Proxy Media - These are files that are only 1/4 of the quality, small, easy to play back. These can be deleted and regenerated any time without losing anything vital. Only create them if you need them. They're only made when your Mac won't handle the native format of your file.
http://help.apple.com/finalcutpro/mac/10.2/#/ver2fd7a8b94
Optimized Media - These are full quality ProRes files, which are much easier for your Mac to play back, than some of the more highly compressed codecs cameras use. Only generate these if your Mac won't handle the native files you're shooting with. The problem with deleting these, is if they're your ONLY copy of the original media. If you import your video files, do NOT select "Copy To Library", and DO select Optimize Files, then deleting Optimized Media will cause you to lose EVERYTHING and be screwed. I just had an editor at our TV station do this without thinking, and lost a whole episode of a locally produced TV show. He doesn't work for us any longer.