The short answer, as of Dojo 1.3:

• Internet Explorer 6.0-8.0
• Firefox 1.5-3.0 (Dijit supports only FireFox 2+)
• Safari 3.1
• Opera 9.6 -- (Dojo core only)
• Konqueror 3.5+ -- (Dojo core only)

The longer answer:

Check the release notes, e.g. http://dojotoolkit.org/book/dojo-1-3-release-notes

As of Dojo 1.3, Mozilla variants other than Firefox (e.g. Minefield, Iceweasel) are not supported.