Flying out of Palm Beach International airport a few days ago, I discovered that another man - one most frequently described these days, in that obscene and oxymoronic phrase, as "having a good war" - was flying in, glad-handing everyone, with his girlfriend. The 57-year-old, still known solemnly to New York Times readers as "Rudolph W Giuliani" but to everybody else as "Rudy", had just completed eight highly eventful years as mayor of New York. And his last day in office was characteristically frenetic: he had completed five television interviews before 8am, then attended the funeral of yet another fireman killed on 11 September (this was around his 100th funeral since that day), followed by a ceremony for swearing in new firemen. He opened a new police station, rang the closing bell at the New York Stock Exchange - and finally left office to the sound of firemen playing Carly Simon's "Nobody Does It Better" and to the skirling of Irish bagpipes.

The man chosen as Time's Person of the Year for 2001 - over the head of not only Osama Bin Laden, but also George Bush or Donald Rumsfeld, lest we forget - was bound for Boca Raton, the upmarket nouveau resort where the very first fatal case of anthrax occurred. But Rudy was not there on official business: he was starting his new career as a private celebrity, earning (I'm told) $100,000 just to speak briefly to a private meeting of General Electric employees. The latest star of the Washington Speakers Bureau agency is rivalled in pulling power only by Bill Clinton, who also still rakes in around $100,000 per speech; put together with a $3m books deal with Talk Miramax, Giuliani was not doing too badly in his first days out of office for a man described not long ago by his divorce lawyer as too poor to rent or buy his own New York apartment (in his final months in office, bizarrely, he lodged with a gay couple).

Not that too many Americans resent Giuliani's new fame and fortune. On the contrary, Rudy is now a hero wherever he goes - and deservedly so, given his behaviour from 11 September onwards. Unlike so many (from the president downwards), he never appeared cowed by the terrifying attacks on his city, and fearlessly turned up at the flaming World Trade Center before the buildings collapsed and then provided a ceaseless flow of information that was always concise and compassionate. Few who saw him on the evening of 11 September will ever forget his words, said in tones of infinite sorrow, that he could not be precise about the death toll, but that it "will be more than any of us can bear". On 10 September, he was New York's lame-duck, 107th mayor - his final months in office dogged by prostate cancer and a nasty divorce, as well as pending political oblivion. Within 48 hours, he was a world hero.

So much so that he is already being seen as a future presidential candidate: should Dick Cheney be forced by ill health to resign as vice-president (as numerous insiders believe he will), many see Rudy as a shoo-in as President Bush's running mate in 2004. And then, perhaps, as the Republican nominee for the presidency in 2008? In the meantime, he has kept much of his political team together in a new consulting firm, Giuliani Partners (a venture sponsored by the accounting giant Ernst and Young), which will maintain close ties with the running of New York; he remains chairman of the Twin Towers Fund; and he has formed the Rudolph W Giuliani Center for Urban Affairs, a presidential-type library.

Superficially, the portents are therefore good. In two terms that saw New York's population increase 450,000 to more than eight million, Giuliani signed 550 bills while in office. The number of people on welfare shrank by almost half; murders in the city fell from 1,927 in 1993 to 671 in 2000, and reported crimes from 430,460 to 184,111. He inherited a $4.2bn budget gap that is now a $600m surplus. He virtually anointed his successor, Michael Bloomberg, a colourless Democrat-turned-Republican who probably would not have been elected had he not spent $63m of his own fortune on his campaign and then received Rudy's public bestowal of approval just before election day; it was the first time in history that a Republican succeeded another as mayor in the largely Democratic New York. And Rudy has remained a controversial figure even as the hapless Bloom-berg takes office, too. He is insisting, for example, that the 16-acre area that was the World Trade Center must remain a sacred memorial - a task easier said than done for his successor, given that it produced 17 per cent of the city's income tax revenue and provided 25 million square feet of its office space.

But American political memories are notoriously short. Rudy's success came at a time of unprecedented economic boom; that surplus is likely to have turned into another $4bn deficit, at least, when the next figures come out in July. The number on welfare is already climbing again, and 30,000 homeless now seek shelter in New York every night. Notwithstanding his success in using a computerised system known as COMPSTAT to cut down on crime, Giuliani always had a trenchant knack for making enemies; by becoming unalloyed champion of the police and fire departments, he also bitterly alienated blacks and Hispanics. He refused to see prominent black officials, even including the woman president of the borough of Manhattan. He defended the police even when they had done the indefensible - such as the torture of a Haitian immigrant named Abner Louima in Brooklyn police station in 1997, the pumping of more than 40 police bullets into an innocent African named Amadou Diallo two years later, and the killing by an undercover cop of a black security guard called Patrick Dorismond in 2000 (in the latter case, despite Dorismond's known innocence, Giuliani later released details of his minor criminal record to show that he was "not an altar boy").

The outgoing mayor has also led an involved private life, perhaps accruing too much baggage to withstand the scrutiny of a presidential campaign, even in current climes. His father, an Italian immigrant, is said to have been a minor Mafia figure who did time for a hold-up in 1934; rumours about the involvement of Giuliani himself in shadowy Italian-American financial deals continue to bubble. His first marriage was brief and bitter, ending with his wife running off with a black academic - a possible reason, armchair psychologists speculate, for his apparent animus towards blacks.

The break-up of his second marriage to the television anchorwoman Donna Hanover, in 2000, was almost indescribably awful: Giuliani was openly attending official functions in the late 1990s with his new girlfriend, 47-year-old Judi Nathan, without so much as a breath of it appearing for months in the press.

He then called a press conference to announce the break-up of his second marriage - overlooking the courtesy of first telling his wife or children (Andrew, 15, and Caroline, 11). They continued to live in the 200-year-old official mayoral mansion overlooking East River known as Gracie Mansion, while Giuliani employed a notorious attack-dog lawyer, Raoul Felder, to bad-mouth his wife. Felder dismissed Hanover as a terrible mother and a wife who was unsympathetic towards her husband's cancer, adding: "She's howling like a stuck pig . . . they'll have to take her biting, scratching and clawing from the premises [Grace Mansion]".

By this time, the story of the marriage break-up and the abandoned children had become New York tabloid fodder; details of Giuliani's relationship with Cristyne Lategano-Nicholas, a junior press officer who had won rapid promotion under him, also became public knowledge.

So is he a saint or a sinner? The truth is that he is both. The events of 11 September brought out human qualities that even his most vociferous critics of the past now acknowledge; in a true crisis, he showed leadership when it was lacking elsewhere. Just as memories of the atrocities of 11 September begin to fade and St Rudy transmogrifies into yet another celebrity superstar, so the fickle American public will deliver its verdict. And only a foolish pundit would dare to predict the final outcome.