Good question, Douglas
Four reasons came to me right off the bat.
First and foremost, I love watching the world go by from above. I've loved that ever since I was a kid flying commercially. Up there, the world looks so peaceful down below. Watching the sun set as the shadows from mountains and buildings stretch longer, watching cars driving in some peaceful Midwestern town 6 miles below and wondering what those people are doing that day, and (possibly my favorite), seeing a patchwork of cloud shadows overlaid on top of the patchwork of farm fields. I don't know why, but that image has always stuck with me. Maybe because it reminds me of going to visit Grandma and Grandpa in Iowa. I still love it. I also like the peace as I take in my setting - sitting in the sky, drinking a coke, and looking out the window at the desert in the evening.
That was mostly appreciation I've received from airline travel, but the peace and "watching the world go by" is applicable to GA as well. I don't quite get as much of that as a low-time pilot, however, since I'm not comfortable enough to just sit back and soak it in and I don't do many long cross countries. Honestly, I like being a passenger almost as much as being a pilot. Almost. I do very much like the idea of puttering around at 1000 feet over farmland in an open cockpit (or any) airplane though. A sunset flight like that, or down the coast here in CA, sounds perfect. Maybe it's the romantic in me.
A very close second is taking off on a drizzly, cold, overcast morning and breaking out just after dawn. I can't wait to get my instrument rating and do it on my own time. Not the most original thought, but it's still true.
Third, I love the history. The 1930's and 1940's have always been my favorite for aviation. I love the technology and how the 1920's/30's vision of the future manifested itself in some of the most beautiful airplanes ever built (I'll cite the XP-38 as one of the best examples of this).
Lastly, I love the power. I don't imagine there are many aviation enthusiasts who don't love the sound of a Merlin engine, or a couple of twin row radials, or the soul shaking power of an afterburner. Those are the most wonderful sounds in the world.
I've decided that one day I will have an open cockpit biplane, an airplane with a radial engine or two, and an airplane with afterburner, just so I can enjoy all these parts of aviation.