I was born almost 20 years after these bikes appeared so I wouldn't consider myself part of the "normal" fanbase.
I owe my fascination with motorcycles (new and old) to my father, who has always been riding. I was along with him when he went to look at buying what is now my 350 in 1996, so I guess that went a long way towards getting me on the sohc4 honda bandwagon.
So why do I like the 750 over other, especially newer, bikes?
For one, I love the styling of the 60's-mid 70's bikes and the 750 excels in this regard. They looked like motorcycles should, like well styled machines. There was shiny chrome, colorful paint, and polished aluminum. Their engines had to be aesthetically pleasing because they were (gasp!) exposed for all to see. I like that the top end looks like a strong solid lump (something that dohc 4's don't do) I feel this solid look is a direct visual compliment to the torquey nature of the motor, and its reliability.
I like the "flatness" of the top of the bike. There's no ugly step in the seat. The tank doesn't buck upwards or downwards. I like that the tank is big and rounded, yet not big enough to keep that beautiful motor from protruding on both sides. It's fun to look down there when you're riding and imagine all those parts spinning around, making that wonderful power when you twist your wrist.
I like those big round gauges, the same way I love the giant speedometer on a vincent. It adds to the visual strength of the motorcycle.
I love the riding experience. Driving a car has become so bland and predictable and I feel motorcycles are slowly headed in this direction too. I like to think of it as like driving one of those big sports cars from the 20's and 30's ( think W.O. Bentley). It's not light and flickable like the 350, but it is solid and strong. The gearchange requires more deliberate movements than the 350, and there's a healthy clunk that makes me feel like I'm moving large gears in some piece of heavy machinery. The engine has such wonderful character, especially for a four. I can cruise down city streets in top gear just riding that torque and listening to those mechanical noises from an air-cooled motor. There's power all through the rev range, just twist the throttle and go. Hills and wind pose no obstacles. And when I decide to really open it up the sound is positively menacing. It's a loud and aggressive howl, completely unlike the high pitched whine of modern 4 cylinder sport bikes.
I like knowing that I'm capable, through the help of this amazing forum, of solving ANY problem I may have, mechanical or otherwise.
I like that it requires periodic maintenance and adjustments, and that these adjustments are all fairly easy. This forces you to spend time with the bike and get to know it better. I like to fiddle with stuff. I like adjusting my carbs and hearing the bike run smoother, or adjusting the valves and hearing the ticking sound go away. I feel like I'm helping improve my bike and am being immediately rewarded with better performance. What can I adjust and improve on a modern bike besides chain tension? No vacuum operated petcocks for me, thank you. I would rather turn the lever myself. And you can have your self-canceling turn signals too. It's my bike and I would like to decide when to turn them off. And if I forget, then it's my own damn fault and I'll learn not to do it next time.
I love that I pulled a crusty 35 year old 40K mile 750 out of a building, never touched anything inside the motor, and it runs great now with no leaks (individual experience may vary)
I like that it functions perfectly well in modern traffic. There's power to spare and brakes that work.
I'm sure I'll think of more but I really need to do homework now!