I try to keep websites accessible at a minimum resolution width of 768pixels, and working on browsers including IE6+, FF2+, Safari 3+.

The only issue I have is that IE6 doesn't natively support transparent PNG images and I just about refuse to be forced to use 8bit GIFs in their place. I mean, it's possible to do so but when I want to have 8bit alpha, you have to use a PNG. There are several scripts that help by automating a work-around for you but I find it doesn't always work.

http://www.google.ca/search?hl=en&q=png%20ie6&meta= the first few results there should work if anyone is interested. This is the one I usually use if the need arises: http://koivi.com/ie-png-transparency/ but I haven't tried some of the other solutions there so your mileage may vary.

At first I code the site so that it's XHTML/CSS valid. Then of course I check it on all major browsers like IE, FF, Chrome, Safari and Opera. I also use www.browsershots.org to check the appearance of my sites in different versions of browser, like IE6.

I actually support all browsers, but I personally use Mozilla Firefox. It doesn't crash at all times.