There's a nifty HTML5 Showcase site that shows some cool demos of what's possible with HTML5.
Unfortunately, at the moment you probably can't view it in any browser other than Chrome.
The first page tells you whether your browser can handle the various demos. (In some browsers, that first page may not load at all; in others, it should show you which features are supported and which aren't.) If your browser can't show the demos, all is not lost; see below for a link to a video.
The best of the demos, in my opinion, is the GAL 9000. Follow that link in Chrome, then wait a little for it to finish loading, then click the Play button in the Options box at the upper left. (For those of you who skimmed directly to this paragraph: if you don't see an Options box or a clickable Play button, then your browser may not support this demo, so go to the main page to check your browser.) For best visual effect, deselect the ”show canvas?” checkbox.
It's a fun demo just to watch and listen to, even if you have no technical background. But it's also got nifty technical stuff going on; for example, most of the visuals are done in HTML5 and CSS, without the use of image files.
The demo site started life as a Google I/O talk by Eric Bidelman and Arne Roomann-Kurrik in May of 2011. If your browser doesn't support the necessary HTML5 features, you can get a taste of what the demo is like by watching the video of that talk, starting around 41:44. Unfortunately, the audio is very quiet, and they only play a few seconds of it, so you don't get the full effect.
Those of you who are interested in the technical aspects of this stuff may want to watch the whole video; Eric and Arne give lots of good info about HTML5's capabilities.