In 2001, Sega announced to the world that they would be stopping manufacturing of their latest (and final) console, the Dreamcast, and would be reworking themselves into a third-party company. That meant that their famous franchises (Sonic, Phantasy Star, Jet Set Radio) would be coming to the Nintendo GameCube, Sony PS2, and Microsoft Xbox.
But that didn't really happen immediately. Sega essentially became a second-party developer for Nintendo for a time, despite the mouthwatering prospects of the insane sales of the PS2 or the better hardware of the Xbox. Sonic Adventure and its sequel were ported exclusively to the GameCube, and both Billy Hatcher and the Giant Egg and Super Monkey Ball were Nintendo exclusives.
So, what might have happened if Nintendo bought Sega? Maybe the reason this happens is that the Big N realizes they made a bad move not buying Rare in 2002, and swoops in to secure some more exclusives during the tumultuous years of the GameCube. Would this lead to Sega continuing to develop quality games instead of OTL travesties like Sonic '06, just only for Nintendo? How might the hardware limitations (but the added motion controls) of the Wii force them to innovate?