My personal record is two battery replacements (AppleCare, both due to capacity being below spec given the number of charge cycles*) and two logic board replacements (GPU failure, first under AppleCare and then out-of-warranty due to a recall) on one MacBook Pro (2011, 17").

* Incidentally, I've received at least half a dozen battery replacements under AppleCare over the years for this reason, going back to the original Titanium PowerBook G4. As far as I can tell, leaving a (Power/Mac)Book plugged in, closed, and running most of the time kills batteries in a warranty-preserving fashion.