Portrait has a 2 player mode, but it is simply a flat and short boss rush area. I tried it with a friend, and it actually lagged pretty bad when we tried it.
Order of Ecclesia has a race to the goal mode, but it's a non combative type of 2 player.
The fangame I was developing had 2 player mode in it. It worked pretty well for what it was, but I can see the need to have an over the net mode, where each player has their own screen. Player 2 had 'Tails in Sonic 2 syndrome' to a small degree, where Player 1 had the priority and Player 2 was on a 'leash' to Player 1. It wasn't too bad most of the time, but when things got heavy, especially if you're in a 2 screen room fighting, like a boss room, player 2's 'leash' got in the way of things. Also for vertical platforming segments, player 2 sometimes just couldn't keep up with the action forcing the level design to be dulled as a result. It basically turned into a one player game with someone else watching. One player could go into 'inactive' mode where they 'teleport out' while the other player does an action. Like how you can 'put away' Jonathan or Charlotte in Portrait. This really was counter-intuitive to the 2 player experience though, and if I were to revisit this game I would have to include net play with two separate screens to compensate for these limitations or remove the 2 Player mode all together.
If it was separate screens over the net, which I didn't have the time or budget for, it would have worked out great though. But alas, never meant to be I suppose. I had to abandon it to move on and actually start my company.