Ignoring the IE case, are there any other browsers that can't understand the application/xhtml+xml content type? And what about the search engine spiders?
I could not find any answers on the web that would not be a few years old and thus possibly inaccurate.
Edit: Somehow related question: http://stackoverflow.com/questions/278746/what-problem-does-xhtml-strict-solve
If you ignore 80% of the market (yes, IE) then XHTML is very well supported, and search engines have no problem with it whatsoever (after all, XHTML is a lot simpler to process).
Overall, XHTML support isn't really a problem. IE doesn't support it, but as long as it's served as a contenttype it does understand, will render it okay anyway, and everyone else support it properly.
Do you have more specific use cases in mind?
Check ou a related question here: http://stackoverflow.com/questions/278746/what-problem-does-xhtml-strict-solve
Hope it helps, Bruno Figueiredo
Since new browsers are invented at a steady pace, there's no definite value for "any" in "any other browsers".
You have to (1) pick some browsers you think you'd like to support, (2) check those specific browsers.
Look at a page like BrowserShots to see a list of browsers you might be interested in supporting.
Look at Free HTML Validators for XHTML compatibility.
Webdevout has a very good browser comparison on various standards, including (X)HTML.