Surprised no-one has mentioned Wolfenstein, Doom and Quake. The shareware versions only gave you access to the first set of levels, but still had hours of gameplay. (I did eventually end up buying these games, but only after I'd played them a lot beforehand).
My mother is an older gamer, and is very selective in the games she played and so I tend to get games she either doesn't like or has completed handed down to me. I got Portal 2 for free since she didn't really see the point of it (I later discovered that she hadn't got far enough into the game to get the portal gun!) I also got Kingdoms of Amalur and Dirt.
It depends on your definition of free, but back in the days of the Spectrum and Commodore 64, games magazines would feature 'free' cassettes loaded with tens of games. Personal highlights from that period include Chaos (wizard battles from the guy who designed XCOM) include Batty (great Breakout clone)