Can The Simpsons ever be beaten?

Next Tuesday, 17 March – St Patrick's Day, those already reaching for their green comedy wigs won't need telling – sees another The Simpsons first. "In the Name of the Grandfather" witnesses America's foremost cartoon family heading for Ireland, where Grampa and Homer buy a pub. Irish Star Trek actor Colm Meaney is the guest star. It's not the fact that this is the Simpsons' first visit to the Emerald Isle that is making history so much as that, after 434 episodes, this is the first time it has been broadcast in Europe before it has gone out in the US. "In the Name of the Grandfather" will be screened on Sky1 on Tuesday, five days before it's shown in the States.

But isn't this just the sort of gimmick on which, according to critics, Fox's cash-cow cartoon has become over-reliant in recent years? The Simpsons has been under sporadic enemy fire since at least the beginning of the century – in fact since not long after it was hubristically declared by a 1999 edition of Time magazine as being "the greatest television show ever". "Euthanise (sic) this once-great show before quality slips any further," was a typical cry from a long-term fan as far back as 2000. "There's still greatness there, and you get to see a home run now and then, but mostly it's a halo of reflected glory," wrote the New York Times journalist Chris Suellentrop in an 2003 article for the online magazine Slate, under the headline "The Simpsons: Who Turned America's Best TV Show into a Cartoon?".

And these days, despite having almost single-handedly invented the animated sitcom genre (Hanna-Barbera's Wait Till Your Father Gets Home was doing something similar back in the Nixon-era) the show no longer has the field to itself. Not only does it have strong opposition, that opposition is about to grow with the imminent premieres of The Goode Family, The Cleveland Show and Sit Down, Shut Up. But more of them later.

Currently three of the main contenders for The Simpsons' slipping crown are the products of the same network – Rupert Murdoch's Fox Broadcasting Channel – and transmit immediately after The Simpsons on a Sunday night: King of the Hill, Family Guy and American Dad, comprising the so-called Animation Domination line-up. Actually make that two, because King of the Hill – a cartoon about a redneck Texan family from Beavis and Butt-head creator Mike Judge – has recently been axed. That leaves the superficially similar Family Guy and American Dad.

Seth MacFarlane's Family Guy has almost had as many lives as the proverbial cat. Centring around a dysfunctional family (you can see why it was considered a Simpsons rip-off) from the fictional town of Quahog, Rhode Island, Fox cancelled Family Guy twice – first in 2000 and then in 2002 – but strong DVD sales convinced the network to resume making it in 2005. MacFarlane meanwhile, given a carte-blanche by a penitent Fox, came up with his satire on the George W Bush-era mindset, American Dad – about yet another dysfunctional family, this one headed up by a CIA agent, Stan Smith.

"Family Guy and American Dad, while they are amusing and ambitious, they are essentially a string of disconnected punch-lines in search of genuine characters and a connective storyline," reckons Hollywood Reporter's Ray Richmond. I don't entirely agree with that since both Family Guy and American Dad can be darker, ruder, nastier, sharper and often funnier than latter-day episodes of The Simpsons. But I would go some way to agreeing with Richmond when he says: "The only show that comes close to the qualitative level achieved by The Simpsons is South Park."

Matt Stone and Trey Parker's fearless animated sitcom, whose 13th series premieres in the UK tonight on Paramount 1, is (as Rolling Stone magazine put it while celebrating the show's tenth anniversary in 2007) "still sick, still wrong". And its crude, cut-up animation style is by far the most radical of its contemporaries.

But South Park is now way older than its protagonists, the perpetual fourth-graders Stan, Kyle, Kenny and Cartman. What is in the animation pipeline, and will any of it finally topple the 20-year dominance of The Simpsons?

Fox's Sit Down, Shut Up, which begins airing in the US next month, sounds like it has the most promise. Based on a short-lived live-action sitcom from Australia, the animated US version revolves around the staff members of a (you guessed it) dysfunctional high school. "It's extremely character based and has different rhythms than other animated shows like The Simpsons or King of the Hill," says the co-producer Bill Oakley, a veteran from the glory days of The Simpsons.

Sit Down, Shut Up is the brainchild of Mitch Hurwitz, the creator of Arrested Development – the award-festooned live-action sitcom about another dysfunctional family, the Bluths. What is it with American television and dysfunctional families? Or rather, as President George Bush Sr once put it, why can't the US be closer to the Waltons than the Simpsons? But then Americans were too busy listening to Bart, not Bush.

Meanwhile Judge has come up with the wicked-sounding The Goode Family (for ABC this time, and not Fox), about an obsessively green family. The paterfamilias Gerald Goode is "from a long line of over-educated academic liberals", says Judge, who will also be voicing him. Could The Goode Family be to Obama's US what American Dad was to George W Bush's? American Dad neatly surfed the war on terror zeitgeist and lampooned the excesses of homeland security. With liberals now seemingly in the ascendancy, Judge has decided to get stuck into some ecological sacred cows.

And what of the state of racial politics in Obama's America? With a black man in the White House, is all right and dandy in the nation that gave us the Ku Klux Klan? If that seems unlikely then the fault lines are sure to be wittily explored by Seth MacFarlane's Family Guy spin-off, The Cleveland Show, which follows Peter Griffin's black friend Cleveland Brown as he relocates to redneck Virginia. Not that we Brits are to be spared our blushes, as among Cleveland's new neighbours are to be an English family (voiced by MacFarlane himself). Oh, and some talking bears. Expect them to get the best lines.

Meanwhile, just in case we get too carried away, two new seasons of The Simpsons have been announced, taking Matt Groening's creation to within spitting distance of its 500th episode. Will it ever end? "There are no plans to pull the plug for the simple reason that the show remains a massive cash cow in its rerun syndication afterlife," says Richmond. "The show repeats more effectively than possibly any show in history, and it's easy to see why. The characters never age, change little, and learn practically nothing from their pasts. They remain stuck in time."

LET'S GET ANIMATED: THREE NEW SIMPSONS RIVALS

Sit Down, Shut Up
The show, starting next month, revolves around the lives of seven staff members at a dysfunctional high school in a fictional North-eastern US fishing town. Developed by the writers behind 'Arrested Development', the action centres on faculty members (voiced by Jason Bateman and Henry "The Fonz" Winkler, among others) as their egos and personal agendas trump the students' needs. The cartoon characters will have a live-action backdrop.

The Goode Family
Fox having axed his 'King of the Hill', it is perhaps understandable that Mike Judge decamped to ABC with his new show about an ecologically obsessed family. Gerald Goode is an administrator at a community college, and his wife Helen is a local activist. They have an adopted son, Ubuntu, who's from Africa, while their biological daughter is called Bliss. The family dog is (forcibly) a vegan. The show is set to premiere later this month.

The Cleveland Show
Seth MacFarlane's 'Family Guy' spin-off follows Peter Griffin's black chum Cleveland Brown as he relocates to Virginia and moves in with his college sweetheart. MacFarlane has found a way to balance the cast's racial make-up, as Mike Henry, who's voiced the Afro-American Cleveland since 'Family Guy' started in 1999, is white; now, the black actor Kevin Richardson will voice Lester, a white "redneck" neighbour. 'The Cleveland Show' begins in the autumn.