I gona repeat alot of the games alredy said, but heres what i play with my younger brothers:
Mario kart - Pretty fun with 2 players since you can join with both on the net!
Mario Sports Mix - This game has hockey, basket, dodgeball and volley with mario chars, the game is really simplificated but, the multiplayer is pretty fun, and the online is cool also.
Bomberman from wiiware - Any bomberman from either wiiware or VC are very good for a multiplayer experience but for you and your boyfriend together i advise you wiiware one because you can log on the internet with the both of you and play vs other people wich make it alot of fun.
Driift from wiiware - Alot of fun in multiplayer not by the racing itself sometimes but because of the modes of gaming such as stealing the potato, or running from the car with virus.
Wario Ware - Awsome for multiplayer, you have to perform fast actions in few seconds, and make really ridiculous minigames, really fun.
All the gamecube Lord of the Rings - The multiplayer in Coop is awsome, the game is easy and pretty hack and slash type, but its really entertaining.
Any Lego game for the Wii - All the lego games have coop and are really fun to play together, offcourse you should choose one from a movie you both enjoyed, atm you got around there lego batman, lego indiana jones 1 and 2, lego starwars (2 of them if i aint wrong or 3), lego harry potter pretty funny to has 4 of the movies included and in future lego pirates of caraibean.
Donkey Kong Series -Any of the donkey kong games is pretty fun in multiplayer, but the last one "Donkey Kong Country Returns" offers the best experience since its coop.
Kirby epic yarn - Offers a less challenging game than donkey kong, but the essence is the same, a pretty good game for coop also.
Dokapoon Kingdom - Pretty funny Board / rpg adventure kinda game, but its better with more than 2 people and the games are often pretty long.
Mario Party for the wii - Board type of game great for multiplayer fun, also better with more than 2 people but still alot of fun with 2 people.
Worm Battle island for the Wii or Worms 3d for gamecube - Nothing goes wrong with worms games, if you prefer 2d bomb each other kinda game
go with worms for the wii, if you prefer the 3d version just pick the gamecube one.
Monster hunter Tri - Its a fun game but mostly in online mode, if you and your bf both own a wii then you should get this, if not, i dont advise because the local multiplayer is basicly fight the monsters inside arenas, its fun, but nothing like the online /single player experience.
Sin and Punishment 2 - If you like arcade on rail kinda shooters, this is a fun one you can get that looks with local coop.
Dead Space Extraction - On rail shooter / horror game, This one is an awsome experience for coop multiplayer i am sure you and your bf would love to play it together.
Resident Evil (Any less 4) - All on rail resident evils for the wii are awsome coop games, they arent as good as deadspace, but if you like more the series ( assuming you like shooters) any of them is advised.
House of the dead (any of them for the wii) - More arcady kinda feel of on rail shooter but pretty fun also.
Samurai warriors 3 - Hack and slash thousands of enemys with your boyfriend as a team, who wouldnt love that XD
rayman raving rabids ( Any in the series) - Awsome minigames collection kinda game, you die of laughing on the dancing games, or watching the silly rabits animations its a great multiplayer game.
Pikmin 2 -Even tough multiplayer is only versus, the game is really funny, is a rather strategy kinda game on the wii, dont really know how to explain better but you might like it.
Boom Blox party- awsome awsome multiplayer game, i dont know to explain what this is
just check youtube for it.
Wii party - Another funny board kinda game, its not bad, and this game unlike the other board games is more fun for 2 players than for 4 because some of the minigames are designed for only 2.
Pacman Party - Also a board game, its funny, but probably a bit worse than the others multiplayer games.
I am sorry but this is all i can remember atm, Some of these games are pretty old, and you can find them for a bargain much anywere, i hope this post helps.