The characters from a world more than 3,000 miles away became household names - Big Bird, Bert and Ernie, Grover and the Cookie Monster - while their creator, Jim Henson, who went on to develop The Muppet Show, became famous around the world.
Few children's programmes have enjoyed such global popularity.
Today, Sesame Street is broadcast in about 140 countries and works on a franchise basis - with local versions that focus on particular cultural perspectives.
A condition of its foreign licensing is that non-US versions of the show reflect the morals and traditions of the host nation. So Sesame characters have been used to promote HIV awareness in South Africa, bridge the sectarian divide in Belfast and teach youngsters in the Middle East about tolerance.
It is now 40 years since its first broadcast in the US, to be marked by an appearance from Michelle Obama, but its start in the UK was anything but smooth.
The show crossed the Atlantic 18 months after its US launch, but the BBC rejected it because of its "authoritarian aims" in trying to change children's behaviour.
"This sounds like indoctrination, and a dangerous extension of the use of television," said the head of children's programmes at the time, Monica Sims.
TV critic Barry Norman, writing in The Times in November 1971, said it was "neither good enough nor bad enough" to justify all the fuss, adding that the BBC had no need for it because it already broadcast Blue Peter and Play School.
HOW DID IT START?
At a dinner party in 1960s New York, hosted by television producer Joan Ganz Cooney
One of her guests spoke about her three-year-old's ability to recite jingles from adverts
Cooney commissioned a study into the ability of television to teach children basic numeracy and the alphabet
She hired Jim Henson to make the puppets
So Sesame's Street's first British home was HTV and after one series there it was picked up by London Weekend Television in 1971, where it became a Saturday morning fixture. Other ITV regions also showed it, before Channel 4 took it on. But in March 2001 Sesame Street left British screens and has yet to return.
"Brought to you by the letters..." became a household phrase, while a generation of British children grew up knowing that their American counterparts pronounced "Zed" as "Zee".
Today, its presence in the UK is limited to Sesame Tree on BBC Northern Ireland, which was launched last year by Deputy First Minister Martin McGuinness, plus Five's Sesame spin-offs Elmo's World and Bert and Ernie's Great Adventures.
So why is the show itself absent from mainstream schedules?
"It's a different world today and specifically in the UK, due in part to the success of the BBC, there is a very competitive pre-school market," says Scott Chambers, senior vice-president of Sesame Street's worldwide media distribution.
Bert and Ernie can be seen on Five
Children are looking for different things nowadays, he says, but the show has adapted to recognise that, with a constantly changing curriculum and even computerised graphics in some countries.
"There's a certain magic to a puppet and that puppet's interaction with a child and we can't get that with CGI (computer generated imagery) or any other kind of animation and that's important to us. Will Sesame Street ever give up puppets? I doubt that, but we can offer more creative ways to do it."
And why is the BBC still not interested?
The controller of six-and-unders channel CBeebies, Michael Carrington, says it has other shows which cover similar learning themes and values.
"Show Me Show Me, Tikkabilla and Numberjacks are just a few examples of CBeebies programmes which inspire and stimulate a child's interest in literacy and numeracy, or help them understand the world around them.
HOW HAS THE SHOW CHANGED?
Michael Davis, author of Street Gang: The Complete History of Sesame Street
"There's a different pace to the show. When it was created, it was thought the concentration span of the typical 3-4 year old was very short, so the show was frenetic, jumping from one thing to another. Today it's much slower because we know that pre-school children can sit still and watch a narrative and understand it."
"It's television's most organic show, always looking for new developments in education and culture. I'm also impressed by the way the show has travelled and created adaptations to reflect the needs of other cultures. It's one of America's finest exports."
Over at Five, an hour-long programme like Sesame Street is just too difficult to squeeze into the schedules, says Nick Wilson, its director of children's programming. And it's preferable to put British voices on imported programmes.
"The style of the programme is a tad out-dated - there are very few puppet shows around now. Perhaps LazyTown, but that's a very different tempo, although it does have the overt educational message."
Some of Sesame Street's guests are not recognisable to a British audience, he says, with the "glory days" of Stevie Wonder being on the show long gone.
A look at the list of guests for the forthcoming 41st season suggests there are still names with some international appeal - actresses Sarah Jessica Parker and Eva Longoria, and comedians Ricky Gervais and Adam Sandler.
Previously the likes of Billy Joel, Kofi Annan and Beyonce have graced the street, to the delight of parents. Comedian Robin Williams appeared six times, including a memorable appearance in 2000 telling Elmo some imaginative uses of a stick.
We had Blue Peter, which was like learning at the feet of a very strict headmistress
Tim Teeman TV critic
Tim Teeman, television critic at the Times, says he loved it as a child.
"I don't know if I learnt anything but I felt like I was learning something. If you grew up in a boring, white British environment, it showed you a place with black faces, different cultures and creeds and people living together in harmony.
"It was the first time I ever saw New York and it looked like this really cool place. This street where everyone knew each other's names. It introduced all kinds of things to kids, like community, getting along with different kinds of people and learning about issues."
Part of its success was due to the way it did not talk down to children, says Mr Teeman.
"We had Blue Peter, which was like learning at the feet of a very strict headmistress. Children are talked down to on Blue Peter - 'Do this and do that and this is what we've learned' but Sesame Street says 'Come on in, we're all the same here'
"This notion of equality about age, race and gender is great because as a child, there are so many barriers between you and the adult world."
But homegrown global successes, such as the Teletubbies, probably contributed to its demise, he says. British television simply became adept at making such shows and stopped looking to America for inspiration.
"Also, kids are a bit more knowing now, so would probably think 'Who's that annoying Big Bird?'
"The great genius of Jim Henson and his workshop was that they made something that doesn't date, in my opinion, but maybe for today's generation of children they want something quicker and flashier.
"Sesame Street has a DIY aesthetic, which I love, but people don't identify with that any more."
Add your comments on this story, using the form below.
I grew up watching Sesame Street and even remember having an argument with one of my first teachers at school who insisted "zed" was not pronounced "zee", despite my very coherent argument that "Big Bird said it was 'zee'" Jamie, Poole, England
Sesame Street brought real learning to kids TV in the way that none of the current crop on any channel do. Can anyone imagine any using lines like "zero is a number" or counting past 12? They are all about entertainment and marketing. If there is no audience for Sesame Street in the UK then it is a sad reflection on us. Sarah Bolton, Epping
My children loved this programme. They are all grown up now, and my eldest son and his three daughters, all aged under seven, moved last year to Boston last year. Their favourite programme there? Sesame Street. Bring it back for my grandchild here!! Glenda Morse, Wellingborough, UK
Sesame Street for me stands out as a beacon in value rich, educational television. I didn't watch it very regularly as a child (I am 34) but I have strong memories of its message on diversity, the importance of supporting one another, and generosity of spirit being an important part of life - I think an example of that rare but wonderful set of circumstances when an idea is borne of sound moral objectives, and this becomes an ideal infecting all who are involved - the resulting whole becoming much more than the sum of its parts. I am glad to have seen this programme and thanks those repsonsible for producing it for their integrity. Murray Soper, Lewisham
I think the answer to your question is that it was the characters the UK public loved, not the series. And the Muppet Show provided that. Simple. John Lewington, Bath
"Sesame Street has a DIY aesthetic, which I love, but people don't identify with that any more." One way to find out, repeat the Muppet Show. Many people are still very fond of them. Jay Furneaux, UK
The fact that the man responsible for CBeebies quotes "Show Me Show Me", "Tikkabilla" and "Numberjacks" as comparable to Sesame Street shows just how far removed from reality the BBC has become. My two-year-old watches clips from the show on the brilliant website and we are sad that we can't see it in the UK. Trouble is that the BBC is full of nice, white, middle-class graduates doing "worthy" stuff they think we should all like and the commercial channels want a 20-minute, cheap filler between the adverts. Sad stuff. Richard Glover, Redruth
How upsetting! Sesame Street was a personal favourite of mine as a child and it is sad to see our children being denied such a gem of knowledge. The notion that our children would reject it is utter nonsense, how many children today are still captivated by the muppets or by puppets found in toy stores. My little cousin, who has just turned three, is fascinated by real life moving puppets and people. The lessons learned are still vital to today's society where the worlds community is much more fluid - Britain is no longer simply *a British accent* - it is made up of Scots, English, Welsh, Irish, Polish, African, American, Canadian, Chinese, Japanese, Australian, Pakistan, Indian accents. So surely the message of equality and respect should be being driven home even further? Zoe Gray, Aberdeen, Scotland
I loved Sesame St growing but was disappointed to see this go off the air just as my own son was enjoying it. All of the alternatives shown on British TV just seem patronising or even dumbed down and don't have anywhere the same entertainment or educational quality, where even now in my 40's I can happily enjoy Sesame St I cannot say the same of other children's programming. Alex Bailey, Corby, England.
I could never stand this irritating programme whenever I saw it as a kid, could not relate to it at all. In my opinion, it won't be missed. Mind you, it's not as bad as the cretinous CBeebies programme Numberjacks. Lazytown, on the other hand, provides entertainment, some education, and positive ethical and behavioural messages to pre-school children and is far superior. Doug B, London, UK
We did not "fall out of love" with Sesame Street. Broadcasters who thought they knew better than us took it away from our children. Chris Blackmore, Melksham
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