For $20, you can get the "ORANGE BOX" which includes:
1) Half Life 2 + EP1 + EP2
*My favorite game of all time.
2) Team Fortress 2
3) Portal
Nice variety of games. HL2 is single-player, and while it's older it still looks great and runs well. TF2 is multi-player capture the flag and lots of fine if you like that type of thing.
Portal is also very fun.
OTHER:
You can also filter the $5 and $10 lists, and click METASCORE to put them in order of most recommended.
At $10, these are some great games if you like the genre:
1) Company of Heroes
2) Fallout 3 (requires the 2-core CPU and ifpsclamp=60 INI fix, and to run above 60FPS)
3) Deus Ex GOTY ($7, older but still a great game)
4) World In Conflict
5) Far Cry (#1)
6) Psychonauts (love or hate it I guess. I think there's a DEMO though)
7) The Witcher Enhanced (Witcher #1). (Must disable Hyperthreading for the CPU if you have it to prevent stutter and force VSYNC on in the Video Control Panel)
8) FAR CRY 2 (same price as FC1 but it depends how good your PC is. FC1 is great for less powerful machines).
9) Rainbow Six Vegas (or RB6Vegas 2, or RB6 Three)
10) Fallout New Vegas (better than Fallout 3?.. Requires ifpsclamp=60 fix and run to maintain above 60FPS. Great game though.)
11) Tomb Raider Underworld ($9). I personally really liked it. Not as much as the recent game which costs a lot more.
12) Red Orchestra 2: Heroes of Stalingrad
13) TRINE (PC Demo available)
You can find REVIEWS for all these games online. Again, keep in mind your PC specs if they aren't really high as some of the slightly older games may even be a better choice.