MGS Ac!d and Ac!d 2 are good for how they played. I was really impressed with the TCG factor and the field you played them on. Playing Ad-Hoc with a buddy was fun, especially if you knew how to play and how to combo cards together. If you could do that, life was golden, lmao.
Phantasy Star Portable 2 is Ad-Hoc and online. Careful with online though. Players then to be extremely high leveled (150+) and somewhat rude. Even worse, when their file is hacked, they can infect yours, corrupting your game and forcing to you to restart all over again. But, if you can have a nice play group, PSP2 is alot of fun. It's essentially a handheld MMO.
Killzone Liberation is alot of fun Ad-Hoc and online. You've got co-op for missions, team deathmatch, and free for all. Co-op makes the game super easy, especially the boss fights. Again, with alot of people playing team deathmatch and ffa, games are as exciting and crazy as any other FPS (even though the game is played from an isometric position). There is downloadable content, but I'm not sure if the PSN Store has it. :/
As for hunting games, Monster Hunter is the hardest, followed by Lords of Arcana, and Gods Eater Burst. Now, MH is the first of the genre, demanding skill over stats. You may have the best weapon and armor in the game, but you only got that by being very good and working very hard. Cool weapons and costumes are earned in MH via quest grinding and hunting. You can tell who is a true hunter and who is a hacker by watching how one fights. MH has a very high learning curve. However, if you can overcome that factor, MH is a very deep and rewarding game, easily providing over 100 hrs of gameplay, if not more (ive seen people clock in at 500 hrs+). MH is even better when you have people to hunt with, as battles are life and death situations. Hell, I've fought one monster for nearly an hour (48 min to be exact) and felt such pride and achievement when my gf and I beat it (stupid Kirin). Sadly, there is no online mode with MH, but there is alot of DLC to challenge you and your hunting party.
LoA is, sadly, Squarenix's attempt at an MH clone. Try the demo. If you like the demo, the game shouldn't be too bad. But if not, don't waste your money. It does some stuff different from MH, but alot of it just doesn't match the feel or accomplishment that MH gives you. Personally, LoA wasn't for me. Most likely because I played MH first and LoA just felt like a terrible rip off. I know there is Ad-Hoc on it but I doubt there is an online mode. Also, it recently got a decent amount of DLC to get, all for free of course.
Last is GEB. Personally, GEB is my favorite. Though limited in customization compared to MH and LoA, GEB is, by far, easier and more fluid than the two. You have double jumps and dashes and are able to wield both long range and short range weapons at once. Though limited in fighting style, GEB shines with having a decent range of customization, almost comparable to MH and having a very engrossing storyline. MH has no story what so ever and LoA's story is weak at best. GEB actually gives you a reason to be attached to certain characters and emotional when terrible situations fall upon them. Also, if you're not familiar with the hunting genre, it's definitely a good place to start, as it's the most forgiving of the games. There is Ad-Hoc but very little DLC. On another interesting note, with the people you do play, you can copy their avatar into your game. Offline, you can take them with you. They'll fight like every other NPC, but obviously, they'll be better than them due to weapons, abilities, etc. When you meet back with your friends, they have a chance of gaining parts from the missions you took them with. So there is a slight advantage to trading avatars and meeting for sessions once in awhile.
As far as it goes, thats all the multiplayer games I've tried. Hope this helps.
PS: I'll come back to suggest more good multiplayer games later. Gnites. xD