This is just bunch of completely legal freeware/abandonware releases, not mentioning the obvious ones like Quake Live or Battlefield Heroes, etc.
(SP) Hidden & Dangerous Deluxe
A game few people have played. It is rough around the edges but cool nonetheless. Kinda like an old 70's WWII espionage movie. Think 'Guns of Navarone' but less epic.
(SP) The Suffering
This was a promotional thing from a while back. Requires an active internet connection to play. According to wiki the distribution was discontinued, though the fileshack download is still up. I can't see why it wouldn't work in any case.
(SP) Pre/Ex Fallout 3 Tech demo aka Van Buren
Another odd one; a ghost of what fallout 3 could have been. Not really a game, but still interesting for would-be devs to ponder at.
(MP) F.E.A.R. Combat + Coop Mod
Free F.E.A.R. mulitplayer. Fun stuff, heavy download. There is a F.E.A.R. coop mod that you can you use with this to fight against AI. Should probably work with just one person with a bot match I would think.
Ancient Bungie game. Well liked, but it doesn't seem like all that imo. For a game of this nature it has a nice art style to it.
(MP) Postal II: Share the Pain Multi
Postal II multi is by all standards quite weak, but can be a bit of fun in a pinch. Bot supported.
(MP) Enemy Territory Wolfenstein
Classic team based multiplayer.