I don't think there is an official "supported browsers" list.
DNN just renders HTML and JS and normally all modern browsers should be supported.
(e.g. FF, IE 6+, Opera 8+, Safari etc.)
You could get into trouble with browsers like Netscape 4, but you can ask yourself if you can caal that a browser....
That's about the framework.
For the skins it's al up to the skinner to support the different browsers, with some CSS hack / javascript (mostly for IE6).
DNN from the box does render "HTML transitional", but that shouldn't a problem for most browsers.
You can switch the DTD to XHTML, but since the core modules are VERY "Transistional" it will (without extra modules/ programming) never validate.