I think a lot of Americans think British comedy consists of Are You Being Served, Keeping Up Appearances and Benny Hill.
I've been watching reruns of Are you being served (shut up) since I was 4 years old off and on... The older I get, the less undoable Mrs Slocum becomes.
They think of them as something on PBS. British television is a staple of the public broadcasting stations.
I don't know what is more surprising - that these aired in the States or that people over there like them...
This is the internet! Reason has no place here! Andy Sandberg did a Britcom late last year. A hippy American who marries a good little English Girl, and her parents hate him. Barely funny. But after 6 episodes I did accept that i was enjoying the interplay between the characters.
Britain has a plethora of sketch comedy groups, many of which have been given their own TV shows, but yeah, I can't remember ever seeing anything similar on American TV. Saturday Night Live seems to be the closest you have, although the cast is constantly changing on that, it does feature a fair bit of absurdist comedy though. Kids in the Hall remind me a lot of Python, although they are Canadian of course.
They both have hit or misses. There's probably some filtering for quality or at least popularity before Brit shows get distribution over here. We get dozens of crappy new shows every season that get quickly cancelled off. I'm sure the same is true over there and we just don't see them.
Key and Peel is on right now. What the fuck about Saturday Night Live? That bastard has been running since 1975. In Living Colour was fantastic. Did you ever see the Sketch show? A mildly funny English sketch show, which later sold all it's scripts to Kelsy Grammar who then remade everything in the US verbatim but less funny? Does Robot Chicken count as a Sketch Show?
My favorite right now is Key & Peele on Comedy Channel. It's more understated but Portlandia on IFC is sketch comedy. In thr past there was In Living Color, Chapelle, The State, probably others I'm missing I'm sure. EDIT Guy beat me to it here
My problem with Saturday Night Live is that they use random guests like Johnny Carson or David Letterman would do. It works for TV talk show hosts because they're able to make the conversation humorous without having that burden placed on the guest. SNL however will have various guests participate in a sketch where they follow a script. The problem there is that just reading/acting from a comedy script is not going to make it funny. And since many of the guests are not comedians, or particularly funny, SNL has had a number of skits where non-funny people are attempting to come across as funny. And often times it just doesn't work. MPFC were not special guest oriented, so they didn't have that problem.
That's true that I didn't mention age, but that was my general idea. Those shows you mentioned were fairly common for the 60's, and pretty much ended there. Although I never became a viewer of Third Rock From the Sun, and have my doubts that I would enjoy it, the show does have a similar storyline typical of the 60's where comedies did use unusual, non-conventional families (hillbillies in rich neighborhoods, cavemen transplanted into the modern era, witches, genies, goths, Universal studio monsters, etc.).
As most people have said there's hit and miss in both, and they tend to be made in very different ways. I prefer many British comedies over many American ones, but that's more personal preference than saying "American comedy sucks!".
That and a good portion of Hollywood isn't open-minded. Watch Mock the Week and they trash everyone in politics. The Tories, Labour and the Lib Dems are not safe, whereas (I don't intend for this to spark any kind of debate) if you tried an American Mock the Week, it would be incredibly one-sided and it would be 95% trashing the Republican Party.
Everybody Hates Chris was an excellent historical comedy! But it had to be set when it was set and didn't really have a choice. Chis Rock gave Todd Bridges a job.
While still one-sided but to the right, there is a odd duck panel show on Fox News called Red Eye but it only airs at 3AM(!) on weeknights.