Almost all games have a demo you can download.
No not really. There are not very many game demos out there. Bethesda does not and has never published a demo for any of their games (Fallout 3, Skyrim, etc...). Well, there is a demo for Skyrim, but it's a "gameplay trailer demo". There was a multiplayer demo for Crysis 2 and BF3, but they have been taken offline after those games have launched. A Crysis demo can still be downloaded though.
Most of the games I have owned never had a demo released for it. I think Crysis was the only one.