My answer is somewhat similar to Roy's in the sense that I've loved aviation all my life, and I've loved warbirds ever since I first discovered that Spitfires and Hurricanes were called "warbirds." The first airplane I ever flew was a warbird, at least technically - a 1944 Cessna UC-78B, an airplane that should be ready for its second trip to Oshkosh next summer. (Note to Roy: lots of progress lately, so I think I actually mean that this time.)
My best-loved flying of the last couple of years has been my time in Canadian Tiger Moths (DH-82Cs), also warbirds, though even less war-ish than the UC-78. Regardless of their role - trainer, utility / cargo, fighter, bomber - there's something profoundly appealing to me about being able to fly these airplanes in a peacetime setting. They fly to honor those who came before, those who "flew them when", by bringing history to life.
But, to me, there's another element, the idea that the veterans who fought in these machines actually created a world in which we're free enough to simply enjoy these magnificent machines for their own sake. When I fly a Moth, for instance, I'm savoring the gifts I've been given and celebrating the fact that, thanks to those who flew that very same airplane 65 years before I did, I'm not heading off to war. I'm just an extraordinarily lucky guy who gets to sample some of the best bits of that part of history without the downside of potentially getting shot down somewhere in Europe a few weeks later.
Of course, plenty of young men and women these days are going to war, and I'm grateful to all who serve. I hope their grandchildren have it as soft and easy as I have, and that we see F/A-18s parked on the warbirds ramp at Oshkosh 2075.