Here is an incomplete list of browsers that are known to work well with Drupal core and support all of its features:
• Internet Explorer 6.x and later
• Firefox 2.x and later
• Opera 7 and later
• Safari 1.x and later
• Camino 1.x and later
• Google Chrome
It's worth mentioning here that IE6 has an problem with loading more than 30 stylesheets, and it's fairly easy to run into this problem once you start adding contrib modules.