I have hesitated to weigh in on this post because not being a pilot myself I feel like an outsider and don't want to intrude.
I thought about it and realize the question wasn't a favorite airplane to fly, so as an admirer I can give you my 2 cents.
First and foremost, any flying machine with a powered rotor on top. The sound of a helicopter running up RPM to reach full speed or takeoff speed / full RPM for lift, is the most exhilarating sound in the world. I love that sound. My favorite helicopter? I can't really say, but check this one out, isn't it beautiful? And for sale too at $7.9 million.
I think the F-16 is beautiful from a design standpoint, very graceful / sleek looking but any of the vectored thrust fighters are incredible to watch flying. They walk across the sky while flying straight up like rockets, just amazing.
I am very fortunate to live right here in EAA country and take in AirVenture so it's very difficult to choose just one plane or type.
I used to( 1979 - 80 ) travel to Abbotsford, BC to the airshow there. It was an eight hour drive over the pass from Eastern Washington, but it was well worth it. I saw the debut of the F-18 and the A-10, both fantastic aircraft. I was able to walk through the C5 Galaxy, WOW, that's one huge plane. The Vulcan bomber flew for the show, really cool.
Out at EAA, two of my favorites are the P-51 Mustang and the Super Corsair. Just the sound of those great engines is enough to put a smile on any gearheads face. That big 12 cylinder Merlin in the P-51 and the 28 cylinder Radial, yes, that's four banks of 7 cylinders, in the Corsair. That's got to get any motor freak excited. When they fly, I can just imagine what it must be like to be a pilot and be able to fly those incredible and very historic aircraft. If you think of the contribution to the war effort that the Mustang made. Turning the tide of the war and developed in such a very short time. The history of the Tuskegee airmen that flew them and their contribution to the war effort. Just amazing stuff.
So now that I've rambled on for awhile I might also go into a little more history as well. My dad was a pilot / flight instructor, had his commercial rating. He quit flying the year I was born but he flew in the good old days, J3 Cubs, Aeroncas, Aerocoupes, Navions, etc. He owned a P-22 trainer for awhile, it is now in a museum in Alaska. So I guess the P-22 has a place as well in my favorites although I really never knew the plane, there were pictures of it with my dad and older brother and sister in it hanging in our house when I was growing up. My dad and mom came out to visit and we went out to the EAA Museum. They really got excited when they saw the Aeronca. Apparently they had spent a lot of time together flying around the local countryside in the Aeronca so that too has a place for me although from a thrill factor, it doesn't have much pazazz.