There's a lot of free software out there, and of course that include games! Although free games are not hard to find (Google!) - finding quality games is another story. Some might be lucky enough to know someone with insight, others have to try out a couple of games before finding a good one. I'm going to give you a few right here, right now. You could check out a previous post about this.
Strategy/Simulation: OpenTTD (Open Transport Tycoon Deluxe).
TTD was one of my favorite games for Windows 98 and I became frustrated when it refused to work under Windows XP. It's based on/inspired by TTD but it doesn't contain any material from the original game. If you want you can import the old graphics (requires the original game).
In OpenTTD you build vehicles and transport goods. It's simple to learn but hard to master. In order to build the best and most efficient enterprise, you need to carefully plan where to build stations and what vehicles to invest in. When dealing with trains you have the ability to run multiple trains on the same track, but this does of course require some skill to pull off.
Be prepared for a steep learning curve. Once you get how it works, you'll love it! OpenTTD is a great game indeed.
Strategy/Action: League of Legends
I've mentioned this game before, but it deserves to be mentioned again! League of Legends - or simply LoL - is a DotA-clone.
Be prepared for a fast-paced third-person real time strategy game! You are one of five on your team, fighting an equal number of opponents. You select your champion and purchase what items you see fit (known as "builds"). Each champion has four unique abilities (plus one passive) such as leaping, stunning or absorbing damage.
The Europe realm has a number of issues (so does the US, but not as many). LoL will sometimes force you to play on US servers, giving you a ping at 100-150. They fund the game selling in-game skins and heroes (heroes can be unlocked by playing as well), so make sure you like what they are doing before you support them. It's not unusual for EU to experience a total shutdown or login queues at an hour or two.
Strategy/Tower Defense: Bloons Tower Defense and Vector TD
Flash-based strategy games never fail! Bloons TD and Vector TD are two great tower defense games. Each one will easily provide two hours of playtime if you like the genre.
Tower Defense is a game genre where you build offensive structures (towers) to eliminate enemies from reaching the end of a map. Sometimes you need to do quite a bit of serious planning to win, but it's a very casual genre. If you need more action you should totally check out (although not free) Sanctum!
Strategy/Action: Blood Line Champions
Now this is a game I'm not really into, however it's worth mentioning. It's said to be a lot like the World Of Warcraft Arena. Focus is placed entirely on your combat skills. There are no critical strikes (which is random and not skill) or such.
Make sure to run the tutorial and practice against bots before playing against other living beings. Another steep learning curve indeed!
BLC works just like LoL in many ways, you have a couple of "free to play" champions and additional champions can be unlocked by either paying or playing. Special non-essential stuff can be bought from an in-game shop which supports the developers.
If you happen to try it out, make sure to drop a comment :).
I've written a list of all the game I've ever played (I update it from time to time). Some games there are free, others are not.
If you know any other free games, please drop a comment! (Trials for i.e. WoW doesn't count as free).