Well I don't consider myself rich; I got back into flying after a break of several years, after our mortgage was paid off; we worked like crazy and got it paid off when we were very young (35 years old to be precise) so I was still young enough to enjoy the hobby. I own 100% of my own aircraft, a very high time 1979 Beech Sundowner (aerobatic by the way), but it was in great shape, picked up at a government-run flying school (your tax dollars at work). It replaced a Cherokee 140 as I wanted more payload. Now that my kids are older and starting to leave the nest, I am looking at trading down to a two-seater like a C-150. I did own a Skipper alongside the Sundowner briefly, with the intent of selling the Sundowner, but I got a deal I couldn't refuse on the Skipper ($5500 more than I paid for it the year before, pays for a lot of gas...).
The first trick to flying is never ever own more aircraft than you need. My top limit was engraved in concrete: no more than 180 hp, fixed gear, fixed pitch prop. All to keep maintenance down. I also have a couple of buddies that fly with me. One is a pretty handy wrench, so he does a lot of the grunt work for me (supervised by the AME), in exchange for flying hours on my machine. This keeps maintenance costs down. Now I no longer really need 180 hp and 4 seats so I am looking at either trading down, or taking on a partner.
However I have to agree, this is by far the most expensive hobby; the only saving grace is that the toy's value is stable or increases over time, but the costs likely exceed that increase. My other hobby is collecting model trains and I can assure you that's a lot cheaper!!!
I do have to ration my flying. At 40 liters per hour and $1.50 per liter, that's a lot for fuel. I usually fly with mates who are willing to chip in for fuel. The rule of thumb: you will get invited for a ride once, but if you don't chip in for fuel, you won't be invited again. I make one exception to the rule, a retired chap in his '80s who was flight engineer on Halifax bombers in the war and had to sell his plane years ago (still has his medical though!). I figure I owe him, not the other way around. He had a multi-IFR rating so he's also fun to have a long, we always play at shooting some instrument approaches (in VMC of course...I have night and VFR on top ratings only).
Anyway I figure I'm good for a few more years yet, and if I downsize to a 100-115 hp two-seater I'll be in the air for quite a few more years, God and the Mrs. willing...