Re: Can you play the sims 3 without the disc?
Yes.
Download the Origin client and input your registration code to add it to your games (if it was not an Origin purchase). If it was an Origin Purchase your game will be there. You will need to uninstall the physical disc copy of the game you have installed on your computer and install the game from the Origin client as a digital download. For more info see this article: http://answers.ea.com/t5/The-Sims-3/FAQ-Lost-and-broken-DVDs-and-missing-serial-codes-What-to-do/td-...
Hope this makes sense. Best of luck.