Do you test your applications under multiple browser settings? Do you use test tools that tell you why your site might be problematic?
Firefox has very useful WebDeveloper add-on. Lets you disable/enable various features of the browser on the fly. You can check how will your app work with cookies disabled or in 800x600 etc.
We use a couple of different machine images with IE6/IE7/IE8 FF2/FF3 Chrome, Opera & Safari for windows installed on them.
For developers, most have IE7 & Firefox installed. The Firefox Web Developer Add-in is handy. As is FireBug, Y-Slow & HTTPFox.
We'll target most sites to 1024*768 and then test to see they look fine @
1280*1024
1280*768
1920*1080
1920*1200
For simple UI Interaction, we've used Selenium in the past for automated/macro testing
Besides testing various resolutions I also test with different DPI I've found its common for offices to use 120dpi on their workstations which can break sites in IE especially.
I usually test pages with designs which are critical for browser-compatibility in browsershots. Try it yourself: browsershots.org