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I use a few others from time to time, but those are pretty much it for me. (Actually, I don't have IE7 yet, but I'm thinking about grabbing it sometime soon.) If your site works for those browsers, you've probably covered better than 98% of your visitors.
Check in IE 4 and Netscape 4 and 6 to see how your site degrades in older browsers. Normally an unstyled page is best if you're using much advanced CSS.
Also, if my pages look good in all test browsers, and validate correctly, can I feel confident that my site will still look good in future browsers (or some other versions of the same browser that haven't been tested)?
Who knows? The idea behind validation is to ensure forward-compatibility. I consider that an impossible order and will probably always test my site in new browsers as they come out.