A really neat and cool online "game" (I use the quotes because it's sort of more like a mock country/nation/society) is the Universal Triumvirate. I've been a member for a while and I can tell you it's a really fun community. You can do all kinds of things on it, everything from starting a mock business, running for political office in elections, being a lawyer, making art, even working as an economist in the stock market.
It's kind of like an RPG but there's so much more to it since it's totally open and web based (instead of graphically based), if you want more information PM me or just check out the site I linked to above, it's really fun and definitely worth checking out if you've got the time!
Karma Online - karmacp.joymax.com (Download)
A very interesting FPS shooter. If I had to describe it, it would probably be a mix of Counter Strike and the classic Call of Duty. You have old guns and new guns, and there are some very interesting characters. I have been following this game for awhile, but I have no played it in a couple of months.
I'm a little lazy and i don't really feel like looking to see if this posted or not. But I don't really know i need a link, but then again, we have google for that. It's a great computer game called World of Tanks. It's a free MMO,FPS,Strategy game that is addicting.
Shadow Era is a 'magic' style CCG (or TCG) where the basic idea of the game is you select a hero, this could be a human mage or a shadow wolf or a lot more, and depending on which race you are (human or shadow) and what type you are (mage warrior elemental ect.) determines what cards you can use ranging from allys, items, and equipment. Each hero is immediately put in play right from the beginning and has their own unique ability (which needs a varying number of shadow points) and each turn you draw a card and gain 1 shadow point. In order to use any card you'll need to sacrifice cards in your hand to attain resources, each card has an individual value which needs to be reached in order to play that card, the better ones using more resources. The goal is to get the opposing hero's health down to zero, which can be attained through allies, items, and even your own hero's ability and equipment. It currently has 200 cards which is going to be the base 'set' 150 more are set to release this summer.
A lot of people proabably already know about it, but for those who don't:
Another website full of flash games (which I'm amazed no one's mentioned yet): Newgrounds.
New games are constantly being uploaded by independent game creators or by various flash game companies. There's a heap of awesome flash animations and series as well (also the home of Egoraptor!)
Some good ones to check out on newgrounds:
Portal: The Flash Version
Fancy Pants Adventures (aka FPA)
Flash Element TD
...and a whole lot of others I can't think of right now.
Just noticed there's a Minecraft tower defense game there. Haven't played yet but definitely gonna give it a go.