Re: Switch downloaded EA games to a new computer?
I can confirm worldwidenuke's explanation. Origin and all origin games you own can be installed on as many computers as you want, but only one Origin Client can be logged in at a time. If you play older games that don't require and Origin log in to play (Ex. Mass Effect 2, Dead Space 2, Crysis 2) you can run the games without running Origin, but this will lead to a sync error the next time you try to play the game with origin. (A sync error is when the game data stored in Origin doesn't match the game data stored on your computer. You will have an option to choose which you'd like to use, local or cloud). More recent games (Mass Effect 3, Battlefield 3) require a connection to Origin at all times, and therefore can only be run on one computer at a time.
Hope I helped!