Flash and Java are the most popular ones used for web based games. You can of course make one in PHP, too, but everything depends on the type of game you are about to build.
actually, flash is horribly inefficient and limited, so what a lot of game developers are doing, is that they are using their own plugins, and/or newer plugin's such as unity, to make games. if your going to be making your first game, id suggest using something like javascript. if your experienced with actual game programming, as in C++, C#, than i'd suggest you try out unity, or even the unreal game engine.
I want to develop some games which players play directly on IE or Firefox, no need to install a standalone game on their computers.
are you thinking of developing online games ?then you should go with flash along with support of java
If your interested in 3d games I'd look into blender. There's a plugin called "burster" which allows end users to run your .blend files (which are the standard output files from blender) through a web browser. I've even seen people use blender for 2d games as well. It's got it's own built in game engine, and you can accomplish quite a bit just by using the built in "logic blocks", then what you can't you can script with python. Definitely worth looking into!