What is safe to delete in order for system to work properly? I'm looking for anything that can be deleted and that don't required by system to work properly.
So far I'm delete DVD Player.app, Chess.app, Photo Booth.app, Stickies.app, Dashboard, Launchpad.app and Mission Control.app (still works after reboot with gestures!)

In terminal.app:
sudo rm -rf DVD\ Player.app


What else ?

If you want to free up some disk space: How can I free up some disk space?
Most of the applications you'll delete are going to be restored the next time there is a software update, and even still it'll only save superficial amount of space. For example, the Mission Control, Launchpad, Dashboard, Time Machine, etc. apps are all less than half a meg, and only serve as links to call upon these features via Dock or Finder.

If you want to make a substantial cut on space without making your mac bulimic, i suggest Monolingual, which deletes unused language support (which is usually around 500 MB to 2 GB) and redundant app binaries.

Most Mac apps are "universal," meaning they support both Intel and (the older) PowerPC processor architectures, by having every application contain a binary compiled for each. If you're running an Intel Mac, monolingual can be used to delete the unused app binaries, saving 1-2 GB