Here is an interesting post on what one web developer does to test a site in all of the relevant browsers.
I think that it’s a good general description of what browsers you should test and things to be looking at in each test.
For instance, some of the older browsers (like IE 5.5 and IE 5) aren’t worth your time to make the site look perfect in them. It is however probably advisable to at least make sure your site is still readable and useable in them (even if that means stripping out the JavaScript and CSS).
Generally speaking, this is about the same process that I follow. I’m not nearly as vigilant with all of the smaller browsers though:
When something major (a full page template or a particularly tricky part of a design) is done I give it a quick check in the latest version of every browser that runs natively on Mac OS X. Currently that means Camino, Flock, iCab, Netscape, OmniWeb, Opera, SeaMonkey, Shiira, WebKit Nightly, and any other newcomers.