Are there any? Set in the more-or-less real modern world, that is. Not fantasy worlds. The past decade or two it seems that its the in thing to portray the upper class as villains or terminally stupid. Or both. There are a number of tropes there. No episode of Sharpe was complete without a lengthy diatribe against the upper classes, for instance and Harry Potter had the Malfoys.
Works set in the past but written in the present are fine; those written and set in the past are not. I’ll leave the cut-off date to your discretion.
Speaking of omnicompetent guys who inherited the family’s stately manor complete with faithful butler, the most recent James Bond movie seems to have put a nail in the coffin of Vesper Lynd’s guesses about everybody’s favorite Royal Navy Commander: she figured he went to Oxford or Cambridge without coming from money, but, c’mon.
Harry Potter might have had a perfectly middle class upbringing but he was loaded.
Black Panther, who’s getting his own movie. Wakanda is a fictional nation but it’s worth mentioning. I assume Wonder Woman and Aquaman are too outre to count for this one.
Oliver Queen/Green Arrow? He’s no longer CEO of Queen Industries, but appears to be quite wealthy still. Speaking of which, Ray Palmer is a wealthy good guy and tech genius.
The GREEN HORNET movie came out fairly recently, and revolved around a rich playboy inheriting the rest of the family fortune – prompting our hero to figure you know, as a newspaper publisher with a bulletproof car, I think I can make this city a better place.
This is the best answer so far that isn’t a comic book or similar. (Yes, I know it’s a video game character but she doesn’t have a Batmobile or an Iron Man suit.)
On ELEMENTARY, they keep noting that Holmes has a rich dad who easily foots the bill for his no-need-to-hold-down-a-job-so-I’ll-solve-crimes lifestyle in modern NYC.
Hero, huh? Though he gets double points in a way because not only was he born rich, but then he gave it all up and made it all back through his own hard work.
For more comic book heroes - Warren Worthington (Angel), Emma Frost and the Braddock (Capt Britain, Psylocke, etc) are all wealthy.
