Are there any famous males who could reasonably be considered equivalent to Paris Hilton or Kim Kardashian, in the sense of being famous not for any particular reason that traditionally people are famous for?
George Clooney?
Mediocre actor at best. Witness Gravity.
OK, lets not just list actors and musicians we don’t like, please.
I can’t think of any equivalents. Sadly, I think it’s because men aren’t as noteworthy for just being rich and (at least somewhat) attractive.
How about Donald Trump ? Sure, he’s rich and very good at pretending to be a successful entrepreneur, but there are plenty of rich white crooks out there. Few of them are quite as media saturating as The Donald.
Plus, the the core of Hilton and Kardashian’s fame was their sex videos. Much like (straight) porn, the stars are the women, not the men.
Note that the guys who fucked Paris and Kim didn’t get famous, as far as I know.
Never really rich, and only famous for 15 minutes, but how about Kato Kaelin?
Bert Convy.
Doesn’t Kim Kardashian have a brother who’s famous for being Kim Kardashian’s brother?
Rob Kardashian?
How about Ryan Seacrest? Okay, he’s a “host” on a TV show but Hilton and Kardashian have also had TV shows. Seacrest doesn’t act or sing or dance - he’s just sort of present.
I think Seacrest is a major show producer, not just a host.
RuPaul - Famous for being a famous female impersonator.
<shrug>
Brody Jenner would be the closest thing but I’d argue that the hosts of various reality TV shows are also famous for the sake of being famous. Carson Daly, Ryan Seacrest, Jeff Probst, and Chris Harrison.
As far as heirs go, Ozzy’s kid Jack Osbourne had a fleeting moment of fame. It is interesting that it seems like the ladies get more notoreity. George W Bush?
Kato Whatever – they guy who was hanging out with O.J when all the trouble went down.
Kaelin? 
Ray J is famous or was. I don’t know who starred with Ms Hilton.
Although he was an actor, for quite some time, George Hamilton was mostly famous for dating one of LBJ’s daughters and having a good tan.
John F Kennedy Jr.
David Eisenhower was mostly famous for his grandfather and fiance.
Leif Garrett.
Not sure why this makes me think of that but : Fabio. Famous for being famously pretty and appearing on the cover on every bodice ripper ever. Has appeared in TV shows and movies - almost always as himself, being smoulderingly pretty.
Once upon a time, there were men who were famous just for being rich, driving fancy cars, and dating beautiful or wealthy women: playboys. I can’t think of anyone like this nowadays.