Usually those sorts of browser games are done as either a flash object or java applet, minecraft for example is usually played as a standalone java program but there is a java applet playable in browser (link to free version thats played in browser: http://www.minecraft.net/classic/play). Only thing about using flash or java applets is that the web browser will require additional plugins and the user will have to have flash or java on their systems, not usually an issue anyway.
I've recently started having a play around with Moai which is primarily for 2D games and I've been very impressed.
what is moai? is it just a cloud storage? or do you just put your game on that cloud for people to use?