By browser game I mean actually in-browser, not a flash game that's embedded in a HTML window, but a game that plays out over several HTML pages and has to reload when you take an action. For me it's Kings of Chaos. It's nice and simple, but incredibly fun and addictive to play. The design of the site is nice too, that's always an important factor, otherwise you end up with an information induced headache :P
Blog for Wallcat Games, a new indie game studio: http://wallcatgames.wordpress.com/
DDTank is a cute MMO browser game with no need to download. With simple keyboard operations, you can interact with or fight against your friends, and experience more fun during the fight. A great number of costumes in shops enables you to customize your character with various cool outfits. DDTank features hilarious tank fight and various weapon effects which will be greatly reinforced with power-ups. The perfect combination of nice graphics, relaxing music and funny sound effects make the game more cute and lovely.
Real of the Mad God. I actually don't play it anymore but kept my interest for a LONG time. It's "kind of" a fantasy action rpg style, but sprites and 2d. On death you lose everything but you do have a bank to put extra stuff in. It got a little worse when they added in the cash shop but all in all is still a great/fun/addictive game.