I'm going to deviate a bit from my standard format today and just talk about something cool and free that you might not be taking advantage of. Now I have kind of a love/hate thing going with free gaming. On one side, I fear that having high quality free games around makes people feel entitled to gaming for free instead of cultivating an expectation that if you want something good, you'll need to pay people to make it. On the other side though, I foolishly spent my life pursuing game making instead of doing something that earns money like I dunno - baking or sanitation work, so having fun stuff around for free is quite useful. I guess I'll just recognize I can't really change it regardless, so I will simply be bitter and play some good free games.
On that note, here's a site you should have bookmarked: www.kongregate.com
Kongregate is an aggregator, which means it scoops up free Flash games from a variety of sources and provides them in one location. It has a ton of games of every size and style available for public consumption. Now many of these are fairly low quality and not really worth your time, but there are also a huge number of absolute gems buried within the collection. These actually aren't very hard to find, since Kongregate does a pretty good job of putting them right out front with their Featured Games, and you can always search the highest rated lists by genre to find games you'll like.
Kongregate then wraps these games with a lightweight achievement system. Basically points, levels, and badges that don't particularly mean anything but make you feel happy. They also throw in some random unlocks on their site-specific card game (Kongai), that you'll probably want later.
Ok, so now you've got the basic idea. Lots and lots of Flash games with a better percentage of higher quality stuff than on the majority of similar sites and some really damn good ones mixed in. Got a little time to kill and want some random fun? Head over and try something out. To get you started, look up these and give them a play:
Sonny / Sonny 2 : You play as a zombie with memory loss in this turn-based combat/RPG. The first guy who talks to you calls you 'Sonny', so that's your name. Nice skill system, classic japanese-style RPG combat, and just all around too good for a free game.
Gemcraft : If you haven't done so, there's an entire genre of 'tower defense' games you need to try out. Whether or not you've already done this, give Gemcraft a try. You place gems in towers to shoot at the attackers with a variety of gem types for different abilities. Its massively long though, so don't feel compelled to finish it. Just savor the experience while you have the urge.
Epic War : I believe there are 4 Epic War titles built now and they're all pretty good. You play as one side of a big battle and churn out units to take out the other side. There are very few commands in the battle so its much less about micromanaging your units and more about monitoring the flow of battle and spell use. Between levels you'll get to unlock and improve powers and units and customize your army to your preferences.
Momentum Missile Mayhem (2) : Stuff explodes and BOUNCES! Simple mechanism makes for very enjoyable play. Typical minor enhancements and unlocks, but the key remains the joy of knocking stuff around and causing it to explode.
Kongai : Kongregate has its own strategic collectible card game associated with the site and it is very well made. Think of this like rock/paper/scissors on super-steroids. Each player picks three heroes who come with four special moves and a single item. You play against another player and simultaneously select your action for the round. The server then shows you how those actions interact. The balance is good enough (not perfect, but what is?) that games are really decided on how good you are at guessing your opponent's actions and outplaying them.
PlanetDefender : A constant stream of missile-shooting spaceships attacks your poor hapless planet which you must coat in defensive structures. You'll need to carefully weigh the tradeoffs of building lower strength structures for short term advantage or saving for larger stronger items or researching new options. This is another example of a simple mechanic that is well used to make for compelling gameplay.
The Necronomicon : Based on the Cthulhu mythos, this strategic card game has all the tentacled monsters and gibbering insanity we know and love. Using a large collection of horrific events and creatures, you try to kill or drive your opponent insane. What's not to love?
There are many more worthwhile games on the site waiting for you to give them a try, so hopefully I've at least tweaked your curiosity. Don't be afraid to just poke around and try stuff out. The real joy of Kongregate is that it really does have a ton of very good games hidden a few clicks in. Explore a bit and you're sure to find something you enjoy.