One game per system makes this tough...
PC: Medieval 2: Total War Gold
Vanilla Med 2 has about 30~ Playable factions, hundreds of units, about 60 provinces to conquer on the map... it's insane in it's content. I could play this over and over with different factions, trying for different difficulties and conditions. Then of course with teh Kingdoms expansion, you have 4 new campaigns based in the Middle East, Germany, Brittania and Americas. Again, all with their own factions, units and provinces. It's a game that would last me a long time.
Dreamcast: Shenmue II
It had to be on here somewhere, my all time favourite game. If nothing else it would make me feel like a part of a big city while I was stuck on a desert island...
I do have doubts about this one, while I play it once every few years, and still love it, if it was one of my ONLY games, I'm not sure how replayable it would be.
Xbox 360: Mega Drive Collection
Like Barry said, 50 games in one, you'd be silly not to take this with you when you have limited choice.
Wii: The King of Fighters: Orochi Saga
I'm still undecided on this one, but it seems like a good choice for long term desert-islanding. The pack has King of Fighters '94, through to '98 (5 full arcade games), each game has a significantly different system and cast of fighters too. Were I stuck on a desert island, I could see myself continually coming back and learning each character in each game, trying to perfect them.