Tuesday I started going through my Steam games in alphabetical order. I successfully got Half-Life, Half-Life: Blue Shift, and Half-Life 2: Lost Coast installed and running. To cap the evening off, I gave Fallout 2 a brief try (which I'd forgotten on Friday), and it ran beautifully.
Wednesday I installed and ran Darwinia (for which I found a native Linux executable), and Half-Life: Opposing Force.
Then on Thursday I tried to get Team Fortress 2 to install and run, but Steam refused to unpack the game files, instead giving me the all too familiar error message, "This game is currently unavailable. Please try again later." I had no luck getting past it, but I haven't run out of things to try yet.