I have a friend that's using Me to play World of Warcraft: we're talking 2009 here people, for an OS that "died" 3 years ago and has long been considered crap.
*AXCEL216 patching site for Windows Me: the "Me SP1" looks promising.
*She says she's using Firefox 3 to browse, even though the Wikipedia article indicates its not supported on the backend. IE 7 or 8 aren't supposed to work either; maybe there's a version of Chromium that does.
*If you have 512MB of RAM or more, change your MaxFileCache setting.
*Grab the latest DirectX runtime if you want to play games well.