It is a great conversation piece. When you tell your coworkers that you ride a bike older than you -I'm 36- you suddenly feel like they look at you from below, having suddenly risen above the average people that can't tell an allen from a torx bolt.
I got nothing against modern bikes. I would love to have a CBR600RR or a FireBlade, but having a 60% chances of it being stolen I rather stick to something cheaper and not as coveted. I don't think "classic" bikes have character or style, they are just obsolete pieces of engineering. If you are lucky enough to have something like a 70's Honda you have a bike that was ahead of his time so you have something pretty reliable by modern standars. I don't see that many 30's or 40's bikes being ridden not even in a daily basis, but just ridden to rallies. They are suppoused to have the "character" and "looks" of 70's bikes, but they couldn't compete with modern bikes. 70's bikes can compete with modern bikes and that's the only reason why they are still around.
Probably the main reason I like these old bikes is that only those who can mantain them can have them. No matter how much you like them, if you need to farm out every maintenance task on your bike you will end up buying a modern bike with less maintenance, not just for saving money but for reducing the days off because the bike is on the shop. The only ones who can ride a "classic" bike with absolute peace of mind are those who fix them, can set the ignition timing with the eyes closed, and can tell what's wrong just by listening to the engine sounds. Those who have a classic bike but doesn't know how it works will always ride uneasy, fearing something "horrible" will happen and will get stranded on the side of the road.
Owning a classic bike is usually not money-wise. And that's maybe the biggest appeal in my opinion. You can enjoy any modern bike if you have the money. You can buy a FireBlade anytime, and ride the hell out of it. You can buy a sandcast if you have the dough, but to enjoy it you need to know how to mantain it, and that can't be bought, you have to put time to learn and practice it.
They say that the beauty of a marathon -I plan to try it in late April- is that you can't buy it. You can finish it only if you have worked your way to it by training. And that's pretty much what happens with these bikes: you can only enjoy them if you have worked your way by learning how it works and how to fix it. In these days we tend to farm out every single task that seems boring, from bringing the shopping home to mowing the lawn and, obviously, to service the bikes. There are some things you have to do by yourself if you want to be sure they are well done.