By only looking for Flash games, you're limiting yourself to some really good gaming.
The only good Flash multiplayer game I think of is Tactics Arena Online. It's a chess engine but absolutely rocks.. if you're into turn-based strategy, that is.
Off the Flash side, try out Continuum/Sub-Space.. some find it really boring, some really enjoy. It's a matter of preference. Asteroid kind-of shooter except you shoot other players. You'll need about a lag of maximum 280ms to play comfortably. Off this engine are many mods made, some major new facelifts, including one which features a Galatic Civilizations approach (revolving around discovering planets, taken over dominated ones and upgrading your space ship).
Then there's titles such as GunBound. Made for kids and working off an engine like Worms. Eg. Pick your angle, fire and hopefully you land. Miss and you recalibrate next turn. I tried it a couple of times and it's a pretty decent game from a programmers side... if you can bare the 10-year-old approach is another story. I'm not too sure if it's been released yet, but the same company was planning on developing a fighter online multiplayer game running in the medieval era... might be worth checking out if it's released yet.
Lastly... go download some old roms or old PC games. The old PC games can often rival games released today. Not sure if it's just more preference as I was around when they were released, but I'm still able to play such games today. For example, Monkey Island, Day of the Tentacle, Sam 'n Max: Hit the road, Myst... list goes on. If you're interested in that, check out this topic I made. The titles there are beyond holy. Here.
A point I need to make is to check out PsychoGoldfish' Website. He was planning, and most probably working, for months on building a few multiplayer systems so maybe it's a good place to check out. Miniclip.com also has a few multiplayer games.