I don't know, but they are competitors in one huge market: desktop computers (sort of) and operating systems. If there's one company that's successfully taking down Windows, that's Apple (with Mac OS X).
Kind of, but not really. Apple gives its operating system away for free, and sells hardware. Microsoft sells its operating system to OEMs and business customers. They aren't directly competing in the way that Coke and Pepsi are.
And Windows (of some version) still has >90% market share for desktop OSes, so OSX is not a credible threat to Microsoft in that space. Microsoft's biggest obstacle in the desktop OS space is Windows XP.
But Apple is more concerned these days in selling iPhones, which makes them a lot of money. And Microsoft wants in on that (disclosure: Microsoft employee, but speaking for myself).