What games would you play if you had no money, but still had a decent computer and internet somehow? Starcraft 2 - The entire arcade section is free and you can play team games with friends. Starcraft 2 would be one of my recommendations. Runescape - Put tons of hours into this game way back. I liked the old version, before all the updates and stuff. Something about it was very charming to me. Not sure if I would play it now though. I've played other free MMOs and FPSs but a lot of them are like clones of other games. I don't really know what else I would choose. APB Reloaded is popular but it was too hard for me to get into. Played Hawken before it was on Steam so I don't know what it's like now.
There are quite a lot of free to play indie games around. If you like FPS games you could try Renegade-X, they just released the open beta maybe two weeks ago. The beta is obviously free but so should be the full game when it is released.
Oh, there are plenty. Like crimsonghost above I'd say indie games are where to look. There are plenty of good games that are free including flash ones. You don't need to spend a dime if you learn where to look for the best indie games. Sites like tigsource or jayisgames provide a lot of useful information about the new releases in the indie movement. I mentioned flash above. While I know that people tend to associate flash games with trash, and true, there are many trash games, the bar is set so high these days and you can find true polished gems on flash websites. Personally, I'm a fan of adventure games and in this genre there are plenty of free ones.
Team Fortress 2. It is a fully fledged FPS, but free. Some of the mechanics in it are some of my favorite in all of video game history (Rocket jumping especially). It's a really great game, and free as well!
I mostly play games that are free-to-play. Those little Facebook games and a few other things are fun and free. Retro games on emulators are interesting and free, though there can be legality issues with those.
Most games that my son play are free games. I let him hook his xbox up live and there are alot free games their for people to play. My son uses one site where they let you try the games and rate them fro free.
I play Lord of the Rings Online for free. While it takes a little longer when one is playing for free, you are forced to play more of the game. As a F2P model goes, it works well and only the impatient have to fork over real cash to play most of the content. There are other MMOs with F2P models, but I think LOTRO has done the best job of it so far.
I'd personally just play Plants Vs. Zombies, to be honest. There are lots of levels on it so I could just pick any of them each time I felt the need to game, and seeing as I could just aim for a higher score each time, the replay value of this game is virtually endless. Also, they have already released 2 versions of it as of now, and they are continually adding more stages to the second one as well, so I have even more stages to enjoy and look forward to in the future. Besides this, there are also a lot of other great mobile app games that I love such as Asphalt and online pool, and I can just play those with other people around the world and get a different challenge each time because of it, so I definitely can have fun playing those games over and over.