Manhattan used to rejoice in two landmark Jewish-owned restaurants. Elaine's - the haunt of film stars, rock stars and writers - closed down last May following the death of its owner, Elaine Kaufman. That left Katz's Delicatessen as the most haimishe place to eat in the most Jewish city on the planet.

Katz's is the home of the world's most celebrated pastrami sandwich. Its time-honoured slogan, "send a salami to your boy in the army", was coined during the Second World War, when many parents ordered Katz's salamis to be shipped to sons fighting overseas. (The tradition continues today with shipments to troops in Afghanistan.)

The business was established in 1888 by Willy Katz, one of thousands of Jews who fled the Russian pogroms for America. He opened the deli on the Lower East Side, the hub of immigrant life at the time, and it still occupies the original site on the corner of East Houston and Ludlow streets. It was enlarged in the '50s but has not changed much since.

The current owners, Fred Austin and his brother-in-law Alan Dell, took over from the Katz family in the deli's centenary year, 1988. Now in their sixties, they are grooming Alan's 24-year-old son, Jake, to succeed them.

Entering the deli you are left in no doubt about its popularity among America's celebrities. Their smiling photos, posing with Fred or Alan or Jake, adorn almost every inch of wall-space. Naturally, Jewish faces abound: Ben Stiller, Barbra Streisand, Richard Dreyfuss (although not that embodiment of Jewish New York, Woody Allen, who is more closely associated with the theatre-themed Carnegie Deli.)

Fred Austin comes from a Polish-Jewish immigrant family and was born and raised in the Lower East Side. He sports a stubbly grey goatee and wears a loose, loudly patterned shirt. Jake, in worn jeans and tee-shirt, is likewise stubble-chinned. Their casual air is deceptive, however - they run a tight ship. An employee caught chewing gum, for example, is swiftly reprimanded.

The staff are almost as ethnically diverse as the city itself, and Austin says while he has some Jewish workers, there are also blacks, Hispanics, Russians and Asians. "But I'm down to one Muslim," he notes.

The kosher-style menu has remained largely unaltered since the early days and they still make their own pickles on the premises. Jake, who clearly enjoys the traditional ethos of the place, had his barmitzvah at Katz's and went to Tufts University, near Boston, where he "majored in economics and pastrami studies". He and his uncle crack a lot of jokes.

"We developed as a neighbourhood restaurant,' says Austin, "and Jewish families had been coming here for generations. But now we've been discovered by the world at large and we get everybody."

Katz's fame spread not only through word-of-mouth, but via the movies. It was here that Meg Ryan performed her fake orgasm scene in the 1989 romantic comedy, When Harry Met Sally. An arrow points to the table where Ryan sat with co-star Billy Crystal. Austin says that at least once a week "a group of kids come in to act out the scene".

The deli also served as the venue for Johnny Depp's meeting with his FBI contact in the Mob movie, Donny Brasco. And in the 1977 detective film, Contract on Cherry Street, starring Frank Sinatra, a corpse was found hanging in the meat locker. "But please - that was only fiction," jokes Austin.

He points out that as well as the showbusiness crowd, the deli has fans among the political elite. Four Presidents have eaten here. "Bill Clinton came here," says Austin. "Meant to stay for 10 minutes and was here two hours. Talked to everyone, ate a big meal. About six months later he's back in New York. His motorcade stops outside and a Secret Service man runs in and orders a pastrami sandwich. Then he runs back out to the President's car and gives the sandwich to an outstretched hand."

And yes, there is a large picture on the wall of a smiling Bill and Fred.

It is lunchtime now and the place has filled up. There is a ticketing system which avoids staff having to handle both food and money. On entering, each customer receives a numbered ticket on which all the food and beverages ordered from the different service areas are recorded. The bill is added up and paid to the cashier on leaving. If you lose your ticket, you have to pay a hefty surcharge.

Austin leads me behind the meat counter to watch a Filipino employee expertly carve a hunk of beef.

"He trained as an A & E doctor, you know," Austin remarks. I take this to be another joke. But amazingly, it is true.

On the other side of the counter, customer Alan Meizlik, a 39-year-old executive at a pharmaceuticals company, is eagerly waiting for his sandwich. He wants to know who I am writing my piece for and I say it's for the JC, in England.

"That's fantastic," he replies. "I'm so glad to meet you." Then he adds: "My grandparents survived the camps."

Sitting nearby are middle-aged married couple Robert and Louise Bailey, visiting from Memphis, Tennessee. "But it's not a tourist thing," says Louise. "It's an eating thing. We're eating our way around New York." They had heard good things about Katz's and had finally made it to the deli. They describe themselves as "honorary Jews".

Having finished their meal, they are ready to leave. "Now we're going for a little walk, to digest," Louise says. "Then we're getting a pizza."