HEMPSTEAD, N.Y. -- Sitting face to face in their final debate, Sens. John McCain and Barack Obama clashed repeatedly last night on taxes, abortion and the rough tone of their presidential campaigns.

In the most contentious of their three debates, Mr. McCain assailed his Democratic opponent's positions on trade, health care and taxes as well as raising questions about his associations with 1960s radical William Ayers and ACORN, a group under scrutiny over allegations that it has been responsible for thousands of improper voter registrations.

Mr. Obama rebutted the criticisms and responded with his own familiar denunciations of the Republican's health care plan and his ties to President Bush.

In their discussions of taxes and health care, they also spent a considerable amount of time discussing which one would bring a better future to Joe the Plumber.

"Senator Obama was out in Ohio, and he had an encounter with a guy who's a plumber; his name is Joe Wurzelbacher," Mr. McCain said. "Joe wants to buy the business that he has been in for all of these years -- worked 10, 12 hours a day. And he wanted to buy the business, but he looked at your tax plan, and he saw that he was going to pay much higher taxes."

Giving his own version of that conversation in Toledo, and of his policies, Mr, Obama replied: "What I essentially said to him was, 'Five years ago, when you were in a position to buy your business, you needed a tax cut then.' And what I want to do is to make sure that the plumber, the nurse, the firefighter, the teacher, the young entrepreneur who doesn't yet have money -- I want to give them a tax break now. And that requires us to make some important choices."

The Illinois senator argued that his tax plan would gives breaks to the middle class and spread opportunity more widely. He argued that his Arizona foe's tax cuts would focus on benefitting large corporations and the wealthy.

As the debate went on, both candidates on several occasion addressed "Joe" directly. At one point, looking into the camera, Mr. Obama assured him, "if you're out there," that his own health care plan could enhance Joe's coverage and would not impose new costs or -- as his GOP rival had suggested -- fines for failing to cover employees.

Some of the sharpest exchanges of an often-tense debate came as the candidates addressed the rough tactics that have recurred in the course of their long campaign. Mr. McCain insisted that his opponent had spent more money on negative ads than any candidate in history. Mr. Obama shot back that Mr. McCain had mounted a television campaign composed solely of negative ads.

Mr. McCain seemed intent on goading his opponent throughout the evening. Mr. Obama, while responding to the attacks, sought to portray himself as a candidate more focused on issues such as the difficulties of the economy.

Mr. McCain argued that the tone of the campaign might have been more elevated if his opponent had agreed to his proposal for an extensive series of town meetings. "Senator Obama ... signed a piece of paper that said he would take public financing for his campaign if I did; that was back when he was a long-shot candidate. You didn't keep your word.

"And when you looked into the camera ... and said, 'I will sit down and negotiate with John McCain about public financing before I make a decision,' you didn't tell the American people the truth, because you didn't."

Mr. Obama responded: "I think the American people are less interested in our hurt feelings during the course of the campaign than addressing the issues that matter to them so deeply. And there is nothing wrong with us having a vigorous debate like we're having tonight about health care, about energy policy, about tax policy. That's the stuff that campaigns should be made of.

"What the American people can't afford, though, is four more years of failed economic policies," the Democrat said. "And what they deserve over the next four weeks is that we talk about what's most pressing to them: the economic crisis."

Mr. McCain complained about a statement by Rep. John Lewis, D-Ga., which suggested that the Republican's campaign was encouraging division and hate reminiscent the civil right movement era.

While Mr. Obama noted that he had disassociated himself from some of the congressman's criticism, he pointed out that some crowd members at McCain rallies had shouted remarks such as "terrorist" and "kill him" when his name was mentioned. "And your running mate [Alaska Gov. Sarah Palin] didn't mention, didn't stop, didn't say, 'Hold on a second, that's kind of out of line.' "

Mr. McCain, as promised, brought up Mr. Obama's associations with Mr. Ayers, now a Chicago education professor but during the 1960s a member of the radical Weather Underground group.

"I don't care about an old washed-up terrorist," he said. "But as Senator [Hillary Rodham] Clinton said in her [Democratic primary campaign] debates with you, we need to know the full extent of that relationship. ... We need to know the full extent of Senator Obama's relationship with ACORN, [which] is now on the verge of maybe perpetrating one of the greatest frauds in voter history in this country, maybe destroying the fabric of democracy."

Mr. Obama said the activities of Mr. Ayers that Mr. McCain was castigating had happened when the Democratic nominee was 8 years old. He also said the Chicago educational board on which he and Mr. Ayers jointly served also comprised a various establishment figures, including prominent Republicans.

Of the allegations regarding ACORN voter registration abuses, Mr. Obama said: "It had nothing to do with us; we were not involved. The only involvement I've had with ACORN was I represented them alongside the U.S. Justice Department in making Illinois implement a motor voter law that helped people get registered at [state motor vehicle offices]."

On a night of more dire news for the economy, Mr. McCain contended that the Democrat's trade and tax policies were reminiscent of those of President Herbert Hoover. Mr. Obama countered that, on core economic issues, Mr. McCain promised a continuation of "the failed policies" of the Bush administration. "Senator Obama, I'm not President Bush," Mr. McCain responded. "If you wanted to run against President Bush, you should have run four years ago."

While both candidates insisted that they would impose no litmus test on potential high-court nominees, Mr. McCain said he thought the landmark Roe v. Wade abortion case had been wrongly decided, while Mr. Obama said it should be upheld.