A few of my favourites have already been mentioned (like Kung Fu Chaos) so here are some others that don't seem to have been mentioned yet.
This was sort of 4 way; IIRC you could set up 4 way fights though you could only have two human players unfortunately. It's still a fun game, I guess you could basically sum it up as 3D Rampage, except with more characters and it's more focused with you beating the other players.
People have already pointed out
Jump Super Stars and its sequel
Jump Ultimate Stars, so I thought I would give this a mention.
J-Stars Victory Vs. is sort of similar to War of the Monsters in that 4 way fights are possible, though there can only be two human players locally. That said the online does allow 4 human players fighting at once.
Unlike its DS counterparts, this is on a console (PS3), it's a 3D game and the cast and overall content is probably going to be less than the Jump Stars games. It also hasn't released yet and may not be announced for the West but on the plus you'll be able to import it because of no region locking at least.
This is a straight up Smash clone. It's also available for PS3, 360 and Wii. It's not that great to play but it has quite a bit of fanservice.
This wasn't a full Smash clone (IIRC you had health bars, and no damage system but similar platforming style), ring outs (and ring out effect) and it was also made by the same team (I think). I don't remember it being that fun.
GAF is already pretty familiar with this but I might as well post it. Rather than be a Smash clone, it tried to do its own thing though YMMV as opposed to whether that was a good or bad thing.
I've never played this before but it seems to be only accessed through PSN.