HTML5, CSS3, and Javascript can handle animations pretty well. All native to the browser and requires no plugins.

There is even WebGL available now and can use your GPU for power. Take a look at three.js - Javascript 3D library for some examples of what you can do with.

You can do so much with modern web development now without any plugins at all.

Flash out puts in HTML5 too

Or you can use apps like Hype Tumult Hype Professional