I'd like to see a game that has satellite elements that can be played on portable devices.
Sega attempted this with Sonic for the Dreamcast, which gave you little tamagotchi like things that you played on the portable memory unit.
The newest version of Outrun lets you port your game progress between the PS2 and the PSP editions.
I'm thinking of something like the former, where, say you have a racing game, and you earn enough cash to upgrade your transmission, which gives you a +3.5 in gear shifting speed during a race. Now maybe you cane take your save game on a memory card, plug it into your palm pilot or pocket pc, and play a puzzle game as your mechanic, which will give you a +4.0 if you win.
Maybe an adventure/mystery game will pop up text messages or emails with clues, or give you small little paper puzzles to decrypt things like passwords, in the guise of a 'password cracking' utility, or somesuch.