These have to be some of the most played offline party games amongst my friends.
Wii Sports Resort (Wii) - I was going to go with a Mario Party game first but Nintendo has beat that horse for so long, I just can't. We need more motion control party games like this classic.
Mario Tennis 64 (N64) - Loved the controls on this and it wasn't so heavy on power-ups and gimmicks like later versions.
Beach Spikers (Gamecube) - SEGA put out some cool sports games for a while and this is probably one of the least played but most fun.
Time Splitters 2 (PS2) - 4 player split screen with a great variety of characters, levels, weapons, etc. Next time you have the itch for GoldenEye, play this instead.
Jerry Glanville's Pigskin Footbrawl (Genesis/Arcade) - Only 1 v 1 multiplayer but the chaos never gets old. Anyone can play it, they don't have to like football, games are short, winner stays.