Suppose I’m writing a 2d tile based MMORPG.
Furthermore suppose I hate flash.
Lastly, suppose I only need my code to run in the latest safari, latest firefox, and latest chrome.
What are the limits to what I can and can’t do? (Are there examples of good game engines that only require a recent web browser)?
Look into HTML5 Canvas http://en.wikipedia.org/wiki/Canvas_element
The latest versions of the browsers you mention already support it.