That depends on who your audience is. I don't like having to support old versions of IE but such is life, a large portion of my userbase uses IE as their primary browser and they don't upgrade it to the latest and greatest.
Web game. The main problem is that I want a bit of animation and sound (and later, if budget allows, a lot more... down the road, I'm really aiming for a desktop game feel on your browser).
Dynamically manipulating the DOM and using animated gifs will only get you so far.
The real alternatives here are html5 or Flash.
I'm not ruling out eventual Flash support, but atm, I'm a one man operation, I don't know squat about Flash, I much prefer native browser technologies over proprietary plugins, my time is limited and my priority is to get something out there.
And really, it's not like I'm not giving everyone a perfectly viable, free option (get yourself a modern browser) so I don't feel too bad about it.
caniuse is a great site, btw.
Yeah, I found it in an html5 book I've read. Sadly, it might have been the best part of the book.
Also, if you haven't looked into Modernizr you can get some of this stuff kind of included in browsers that don't support it. It's a really great tool: http://www.modernizr.com
Yeah, that's good for feature detection.
I haven't implemented that part yet (mostly because I need to get some old browser to test it on), but I'll use it to show people with older browser a flat 'update your browser' message.
It's more courteous than to silently allow them to access a web site that has tons of features that just won't work on their browser.