For something that works for the user, OOBE (without add-ins etc); Javascript is probably the only unified functionality that exists between all browsers.
The browser is surprisingly quite capable (at least Chrome is), this is something that Google Chrome is attempting to promote (see http://www.chromeexperiments.com/). Notice some however, that experiments are often laggy or unworkable in other web browsers.
As for a list of things that are and aren't capable; that would take a fair while to compile.
In regards specifically to a 2D tile based game, I wouldn't say it isn't possible, but it may be quite difficult to create. As mentioned before, most browsers (apart from the stand-out; Google Chrome), suffer from limited resources. Therefore resources wise, it may be difficult to implement and would defiantly require a lot of requirement fore planning.