AFAIK, webkit-based (safari, chrome, etc.), firefox, opera, and IE 8 support some, not all, of the HTML 5 features. Things like video are inconsistent as Apple/Webkit want H264, which mozilla is against (they prefer ogg or something) because of licensing issues.
Use feature detection and the HTML5 doctype. I'm not well read, but you can read up some here.
Canvas is supported by all browsers -- except IE, but Google provides excanvas to allow IE to support canvas (it's slower than a native implementation). Canvas provides a location to directly draw on the screen.
For some examples of canvas usage see processing.js and Bespin. Canvas is definitely capable for drawing at a decent speed, excluding the useless IE.