Do all games need patching?

It depends on the game. http://sgt-dan.com provides a list of games and patches. For each game that you have in mind, look it up on the site and see if the patch applies to your circumstances. An unprotected PAL game, for example, to be copied for use in a PAL PS2 and a PAL TV needs no patches. If you have an NTSC game, it might need patching as per what you find on the site.

Most EA games, however need patching (http://www.eapatcher.com).