Unfortunately, Torbutton only works with Firefox right now, and without Torbutton's extensive privacy fixes there are many ways for websites or other attackers to recognize you, track you back to your IP address, and so on. In short, using any browser besides Tor Browser Bundle with Tor is a really bad idea.
We're working with the Chrome team to fix some bugs and missing APIs in Chrome so it will be possible to write a Torbutton for Chrome. The blocking bugs inside of Chrome related to having a working Tor Button are summarized here (https://trac.torproject.org/projects/tor/wiki/doc/ImportantGoogleChromeBugs). These bugs are related to Chrome bypassing the proxy policy (in the case of OCSP (https://code.google.com/p/chromium/issues/detail?id=80722) and FTP(https://code.google.com/p/chromium/issues/detail?id=11227)), browser state related leaks that link the user in incognito mode to that outside of incognito mode (https://code.google.com/p/chromium/issues/detail?id=30877) and fingerprint related bugs that allow third parties to track and link users without consent. This last issue is non blocking and is an active research area, good information on it can be found on the webkit trac page (https://trac.webkit.org/wiki/Fingerprinting). Note that these issues probably are not specific to Chrome and similar issues may emerge from a thorough analysis of any other browser.
The current version of Opera leaks DNS requests and is a known issue by the Opera dev team (http://my.opera.com/desktopteam/blog/2011/04/05/stability-gmail-socks). A thorough analysis still needs to be done.
No support for any other browser is on the horizon.