There have been a lot of TV series that would have been different and maybe even better if they had had the same freedom of expression wrt sex and nudity that are now enjoyed by series such as HBO’s Rome. So, which ones do you think would work well under this rubric?
I’m thinking Lexx and Farscape would have popped a few eyeballs if they’d had free run in terms of sex and nudity. They’re both SF series that pushed the limits as things were. Given free reign, I think they woulda ruled.
Full House.
Gilligan’s Island.
Now you must come up with a credible reason why sex and nudity would have helped. Have fun!
I’d like to see a show like Scrubs that wasn’t restrained by being on broadcast TV.
Aside from the more obvious things like the women all wearing shirts in the immediate post coital scenes, it’d be nice to see a medical show deal with how much shit hospital staff deal with – that is, real honest to god faeces. That and vomit. And blood. And liters upon litres of urine.
There’s also room for lots of humor dealing with patient nudity.
I’m sure you could get some good jokes out of it, too!
Dark Angel - for all the wrong reasons
Star Trek TOS
Insead of just shots of Kirk putting his boots on, we could have a little more.
Brady Bunch.
Okay, okay.
Friends.
Part of me wants to say Hill St. Blues - yeah, you could argue that NYPD Blue did that, but it wasn’t the same so show as HSB.
Also, HSB was revolutionary enough with its large cast and intersecting and diverging plotlines - but if were being done today, it would HAVE to be with a more open approach, per the OP…
Same for M.A.S.H. - fine for what it was and when it was; if re-done today would have to be done with a more open tone…
I Dream of Jeannie.
I Dream of Jeannie. It would have made the whole “master” thing a lot more interesting… 
Chappelle Show
Xena : Warrior Princess. 
Also, Buffy the Vampire Slayer.
L.A. Law. Any of the old Bochco shows, actually. They obviously had plenty of opportunity, and just closed the door on the good parts…
Sesame Street…no, wait…Mr. Rogers!
The Golden Girls nekkid.
HA! now go scrub your brains getting that out of your heads.
Well, if we posit that Full House was the absolute nadir of comedy, that is nothing could be less funny than it, then any change would necessarily have increased the funnyness.
Plus, Aunt Becky was hot, man. And the oldest daughter wasn’t bad either in the later years either.
So, what do I win?
Buffy and Angel, definitely. Plenty of eye candy no matter who or what turns you on.
Star Trek
Married with Children