roguelikes!
Tales of Maj'eyal - http://www.te4.org
Dungeon Crawl Stone Soup - http://crawl.develz.org/wordpress/
and many more (nethack, rogue, etc..) all free
If you are into nice graphics though give the roguelikes above a pass, or start w/tales of maj'eyal. Graphics in roguelikes tend to be pretty primitive for the most part. But the depth of gameplay and class systems are hard to match. Most are pretty hard too, and most have permadeath, so if that's not your thing, then once again - give 'em a pass. Since ya don't have a lot of time though, difficult permadeath type games might be your thing. You sit down, you play till ya die in one sitting (and you will die), you done until next time.
a free TBS - battle for wesnoth: http://wesnoth.org/ (kind of like the old ps1 game - master of monsters, i think one of the developers is who made wesnoth even, iirc).
another place to look for free games of all sorts - http://sourceforge.net, a gathering place for open source games (and open source apps/utilities/etc...). Be careful, many are still in development, so some of 'em barely work, so look @ how finished it is before downloading it or you could end up w/ a pre alpha or some such. But there are a lot of gems hidden in the mix. If you can code at all, or do art, or make music, you can also contribute to the creation of a game here, help design a game the way you want, get yourself into the credits, have something cool to put on your resume.
I'm sure you've heard of it, but there's also League of Legends. Competitive online multiplayer. Starts out free. You can unlock everything but vanity skins simply by playing, so if ya don't mind not posessing the coolest looking skin and you don't mind waiting to slowly unlock the champions you want by earning the points to do so by just playing the game, then ya never have to spend a penny. People are usually streaming the game on various streaming sites, so ya can just check out some streams if ya wanna see what it looks like. I'd avoid it if ya don't have a thick skin though, because although there are a lot of nice players, there are also a lot of people who will whine, complain, blame their mistakes on you, and loudly and w/great verbosity. This is also a game that's good for someone who doesn't have a lot of time, because its a match based pvp game. You play a match 'till one side wins, then you done and can walk away.
edit: free internet chess server, w/ a client like babaschess (that's the one i use). http://www.freechess.org A lot of the 'free chess' servers out there claim to be free, but ya have to pay for advanced features. This one actually is free. You can watch other games in progress, multiple games at a time. Fun to watch the high rating games. You can play against a computer by challenging one of the computer opponents (of various skill ratings) just like you would a real person and it'll auto-accept and just start playing against you.