If Apple worked with Microsoft on their next console, that would be pretty cool. I.E. Apple design and OS, with Microsoft gaming studios, Live, etc. But the chances of that are beyond slim - neither would like to admit the cooperation of the other would be to their benefit.
Apple wouldn't be able to compete with Sony, Nintendo or Microsoft in the console gaming market on their own.
Would be cool though, I can just picture a slim metallic design with similar aluminium wireless controllers, iPod/Phone connectivity, Mini Display Port standard

, and 'Designed By Microsoft Studios and Apple Corporation' in discreet writing under a new logo and name (iConsole, iGame, iBox?).
Hell, they could take on Blu-Ray with a new format if they worked together on a gaming/multimedia device. Start with mainly downloadable content to make sure it would be cheap for the film studios to back the new format, then slowly start releasing discs...
Could make some serious money this way. Plus they could go half/half on the loss they would be selling the console at, thus saving both of them money. Would attract hell loads of free publicity, probably and immense fanbase, you can imagine the support it would generate... In a perfect world this would definitely happen.
Competition isn't always best for the consumer is it?