The kindle doesn't have a computer screen in the classic sense: it's not backlit and doesn't even use the same technology (no LCD, TFT or even CRT going on at all). It uses what, to me*, is the niftiest thing about the whole kerboodle: e-ink pearl. In short, the screen is made up of pockets of ink that are moved around whenever you 'turn' a page. The result is the most 'real book'-like screen that I've ever seen, with excellent contrast and next-to-no glare**.
The Kindle (and other e-books worth talking about) are about as close as you can get to a real book without picking up a real book, in terms of visual comfort. I haven't noticed any eye strain beyond that generated by reading a traditional book: my eyes are tired out by computer use as much as anyone's, and my Kindle's closer to the bookshelf than it is to the desktop in this respect.
* A big, raving geek.
** I've managed to get a level of glare which makes my Kindle's screen unreadable, but only after trying.