I usually aim for IE7, FF, Safari and Opera. Now, I even double check in Chrome but it generally has the same issues as Safari so if you check Safari you're probably safe in most cases. IE6 usually doesn't require too much adjusting to get it to work fine, so I will usually just go ahead and do it so I can sleep better at night. If you get into the habit of doing this and actually do your research to determine the causes of the behavior of these browsers, you'll be able to make adjustments in no time.
Also as far as testing IE6, I've found that
MultipleIE is a good tool to install a standalone version of IE6. I think it goes back to IE 3.01 but going past IE 5.5 is just insane and I usually won't go as far as IE5.5. So you can update to IE7, and install multiple-ie's version of IE6 and have them both on the same PC. I think this is a better solution to what was stated above with the virutal machines unless you actually intend to test in different operating systems as well.
Browsershots was a good suggestion as well, I do donate to them for priority processing because I think it's such a great service, I am in the process of setting up my linux box to be a browser farm for them as well.
Anyway, I hope this helps!