Ok... LETS MAKE SOME MAGIC!
I'll try to categorize these in the way I feel is most appropiate.
Two player epics:
Rebel Strike (GCN) - The entirety of Rogue Leader is available on this game from the very beginning as a co-op experience that is very difficult, very beautiful, and extremely rewarding. It also features a hefty two player vs. mode full of weird ways to blow each other up... Death Star Trench... RACE?! Yes, it's a space shooter.
Timesplitters Future Perfect (GCN or PS2) - Cute FPS with a lot of humor, a lot of explosions, and a lot of multiplayer fun for two to four players. What makes this one special is the story doesn't suck, the engine is good, and it's 2 player co-op the whole way through.
Capcom Vs. SNK 2 EO (GCN) - If and only if you want a competitive game that will get people coming back to practice and compete in tournaments... look no further than CvS2. As one of the most balanced Street Fighter engine games ever, it wil stand the test of time party after get together after boring evening. It features several dozen characters, with several ways to play each; and though fighting is always one on one, you can create an interesting dynamic by letting each player control a fighter, that way larger groups aren't bored out of their mind either. Also, if fighting games are not totally off-base for your friends, you'd do well to check out
Soul Calibur II (GCN) - 3D fighter featuring Link as a character, simplistic gameplay means anyone can be a winner
Super Smash Bros. Melee (GCN) -probably familiar with this, you'd be surprised who all would enjoy it
Street Fighter Anniversary Collection (PS2) - this includes Street Fighter III and the SF movie
Street Fighter Alpha Anthology (PS2) - not extremely balanced but a ton of fun that includes all the previous games.
Four Player Multiplayer Fun:
Bomberman 64 (N64) - Four player game that deviates a bit from the standard Bomberman recipe, suffers framerate slow down from time to time but it's one of the most frantic multiplayer experiences the N64 has to offer, especially since downed players can still haunt their living opponents, possess them, and run them into their own explosions.
Super Bomberman (SNES) - This and #2 are great iterations of Bomberman (if not the best), these support four players (with a multitap, if you don't have one just get the GCN games Bomberman Jetters or Bomberman Generation). You run around placing bombs to kill each other, it's very cutesy but very fast fun.
Mario Power Tennis (GCN) - While not boasting the lengthy co-op of some other games, Mario Power Tennis delivers on everything that made the N64 game great and expands on it with prettier graphics, all new courts (including gimmicks to make gameplay downright hectic), and even a few terrifying characters like Wiggler. There's also another FMV intro that's hilarious to watch, much like some of the other Camelot offerings. This makes a great game amongst friends though, even if they're not into games because it's incredibly simple to learn.
Mario Kart: Double Dash (GCN) - In many ways this game isn't as fast paced as the other Mario Kart titles out there, but the variety of ways to play make it worth a purchase. Four players can choose between each having their own kart, or piggy backing with each other, one person plays gunner and another person drives. This adds for an interesting chariot-esque dynamic as the gunner strafes the kart into passerby in an attempt to steal their items and spin them off into obstacles. Great music, great game design, it's only hindered by the unrewarding singleplayer (but even that features 2 player co-op so lets not complain, it will make for good fun with any friend that has no clue what they're doing)
Super Mario Strikers (GCN) - Whether you're looking for a quick game of soccer or just another Mario sports game, Strikers tends to deliver both. It's one of the best soccer titles that's been produced in recent years, the gameplay is solid albeit basic... you have everything that makes soccer games great but not much else. Bowser interruptions and item useage makes for a more light hearted party atmosphere.
My Absolute Top Picks (for your platforms):
Secret of Mana (SNES) - There is no better co-op experience to this day. You get to run around killing crap and follow a cutesy but gorgeous story. This is what **** like Final Fantasy Crystal Chronicles WISHES it could be.
Super Monkey Ball (GCN or PS2) - There are a ton of these games, perhaps skip out on adventure when it comes to your multiplayer outings but... these games are full of simple gameplay but immense challenge and fun. Few things beat the solid design of these titles, you'd be amazed how frustrating and addicting rolling around a monkey in a ball can be.
Legend of Zelda: Four Swords Adventures (GCN) - This one might be a bit harder for you to make happen. But in the current generation of consoles and over the past ten years of gaming there is nothing more fun to play with four players. Here is a simple game that is oriented around puzzle solving and team work, but throws a monkey wrench into its own design as you and friends compete for gems and vote against each other at the end of rounds to determine who is the best hero.
Dr. Mario 64 (N64) - Puzzlers are never having too easy of a time organizing a game without a handheld in their house, but Dr. Mario 64 is a cheap console puzzler that will accommodate four players and have them tearing into each other with its addictive gameplay. While you'll spend a lot of time separating the masters from the chumps, this is another one that will have the non-gamers crawling back. It's certainly on level with the enjoyability of Tetris.
Mario Party (N64 or GCN) - While it seems an obvious choice, the number of sequels tend to scare people when it comes to these games. Get #3 (N64), or #6 (GCN) for some guaranteed laughs. #6 comes with a microphone that allows the most clammy handed fool to just shout into the microphone to win a round. Teamplay is encouraged but these games have modes that will work for any amount of people you can gather together in one room.
Wario Ware Mega Party Games (GCN) - One of the greatest party games ever made, it's full of simple challenges that never use more than the control stick and the A button. Anyone can pick this up, and as an added bonus it's EXTREMELY cheap. It's certainly bizarre, but don't let the odd art put you off, few games are this fun and even fewer will keep people's attention for this long. Also take into consideration you can play through all the minigames you earn on your own for as long as you can survive for an added bit of challenge. Also enjoy the "Jump Forever" mode, where you and your friends just repeatedly time your "A" button presses until someone finally trips the rope.
Other random recommendations:
- The Tony Hawk series if you haven't played those to death
- wrestling games (Day of Reckoning 2 on GCN, Smackdown 4 or 5 on PS2, WWF No Mercy on N64)
- Sunset Riders (SNES co-op shooter, arcade port)
- Teenage Mutant Ninja Turtles IV Turtles in Time (SNES two player co-op beat'em-up)
- Super Double Dragon (same story as TMNT)
- Star Fox 64 or Star Fox Assault (GCN) - great shooters that support up to four players, no co-op on either title though
- Darius Twin (SNES) - there isn't a better sidescrolling space shooter out there in my opinion, features two-player co-op
- Clone Wars (GCN) - if you are a asucker for Star Wars, the "Geonosis" Academy mode stage is the best rendition of that battle in Episode II that your'e going to get.
- Gauntlet titles (N64, GCN, PS2) - Dark Legacy is your best bet, four player co-op dungeon crawling... kill a ton of enemies, level your guy up; these are not deep games, they're extremely arcade-y but they have a thrill factor to them that is sadly absent from many multiplayer RPGs. It's not without it's humor either, as an announcer tells you when you need food, or when you picked up some sweet power-up. Besides everyone laughs at "Use magic to kill death."
- Zombies Ate My Neighbors (SNES) - obnoxious ass sound and music are not able to mar a terrifying and difficult two player adventure.
- Diddy Kong Racing (N64) - some people dumped this in favor of Mario Kart, but DKR is far better designed than a lot of racers out there, you can fly a plane, float in a hovercraft, or race a car through dozens of tracks in a very beautiful N64 game. It has co-op modes and four player options.
- Dragon Ball Z Budokai 3 (PS2) - hilarious fun that is more about goofy finishers than real competition. Players are invited to customize their character in order to become an even more insanely overpowered beast than they were already. (2 players)
- Phantasy Star Online (GCN) - if you want -real- dungeon crawling, light character building and a ton of obsessing over rare item drops, PSO is that at its best. Not really recommended for anyone that wants to actually use their motor skills though. Up to four players at once.
- F-Zero GX (GCN) - extremely twitch heavy racing game that only experts should really get into. Neat enough music, insane graphics and sense of speed that are hard to find anywhere else. You can also customize your vehicles though, with hand drawn decals as well as individual parts to cater to your particular handling tastes. 4 players.
- Kirby Air Ride (GCN) - quirky GCN party-er, driver around in floaty craft for racing or just tests of flying skill. City Trial mode gives you a few minutes to power-up your rides before a big mini-game competition. Four players.
- Goldeneye (N64) - Up to four players can run around and shoot each other, but you probably already heard of this one.