Use HTML5 and canvas (available on non IE browsers). Modern browsers have very powerful JS engines. It's very fast using tile-like graphics and sprites (images with apha channel).
Making 2D games like those on Genesis and SNES wouldn't be a problem. Many "oldschool" gaming techniques are valid for JS, like tile mapping, scrollings, parallax, hit detections, etc. But now you have more powerful tools.
canvas tutorial: https://developer.mozilla.org/en/Canvas%5Ftutorial
Using images: https://developer.mozilla.org/en/Canvas%5Ftutorial/Using%5Fimages
Game tutorial using Canvas and Javascript: http://webdemos.sourceforge.net/jsplatformer11/jsplatformer11.html
Spaceship shooter: http://29a.ch/jswars/
Tiled Platform game: http://www.paulbrunt.co.uk/bert/
Canvas 3D tetris: http://www.benjoffe.com/code/games/torus/
I did this: http://www.codebase.es/jsgb -> it's a Javascript gameboy emulator (use google chrome to get full speed).
And: http://www.codebase.es/test/snow.php -> a very simple animation demo (snow falling effect)
Also, newer developer versions of FF/webkit have OpenGL support for canvas