Are there any examples of simple games that rely on real time action (as opposed being to turn based), Metal Slug for example, that are massively multiplayer?

What are the technical restrictions of something like this?

I've played dungeon fighter before, which fits your description pretty well. I couldn't remember what it was called, so I some googling, and found some good lists on mmobomb. Their 2d section and fighting sections might not all fit (i see some turn based in the descriptions), but it's a good start.

http://www.mmobomb.com/games/fighting/

What is your definition of "massively multiplayer"?

Like 1000's of players running around in the same 2D level? If not, why even call it "massively multiplayer"?

You will find that the technical challenges will be mostly synchronization issues between the clients and the server. The more forgiving the game design is for sync lag, the better the players expierience will be (and the more money can be saved on bandwidth and server infrastructure).

Dungeon fighter had a massively multiplayer feeling in town, where it probably doesn't matter if things are synced. You could see a wide variety of players running around to different shops and things, with different outfits, and that kind of thing. Then outside of town in combat, it's a smaller scale multiplayer, where a small group could fight enemies together.