(CNN) -- Vote counting has begun across the United States on one of the key dates in the race to become the next U.S. president, with projected wins for each of the major runners
Super Tuesday has some of the biggest prizes of the primary season -- including California, New York, Illinois, New Jersey, Missouri and Georgia -- up for grabs as voters make their party choices in 24 states and American Samoa.
In the Democratic races, CNN projections indicated wins for Hillary Clinton in Arizona, California, Massachusetts, New Jersey, New York, Oklahoma, Tennessee and Arkansas, where her husband was once governor.
Barack Obama has CNN-projected wins in his home state of Illinois, plus Alabama, Alaska, Colorado, Connecticut, Delaware, Georgia, Idaho, Illinois, Kansas, Minnesota, Missouri, North Dakota, and Utah.
On the Republican side, CNN projects Arizona Senator John McCain to win Arizona, California, Connecticut, Delaware, Illinois, Missouri, New Jersey, New York and Oklahoma.
CNN projects Republican Mitt Romney to take Colorado, Massachusetts, Minnesota, Montana, North Dakota and Utah.
CNN projects Republican Mike Huckabee will win Alabama, Arkansas, Georgia, Tennessee and West Virginia.
Clinton appeared before supporters in New York Tuesday night, saying, "Tonight in record numbers, you voted not just to make history but to remake America.
"After seven years of a president who listens only to the special interests, you're ready for a president who brings your values and your dreams to your White House," she said.
She capped her speech with the words: "I know we're ready."
In Chicago, Illinois, Obama took the stage to the strains of U2's "It's a Beautiful Day" Tuesday night, claiming that "our time has come ... and change is coming to America."
"There is one thing on this February night that we do not need the final results to know," he said, noting that all the votes on Super Tuesday had not been counted. "Our time has come.
"What began as a whisper in Springfield has swelled to a chorus of millions calling for change," Obama said. "This time can be different because this campaign for the presidency of the United States of America is different."
Barring a disaster for either Clinton or Obama as the night progresses, neither candidate is expected to deliver a knockout blow because most Democratic races slice up the all-important delegates proportional to the vote
Frontrunner McCain has the potential to enjoy a towering lead over rivals if he takes the bigger states.
So far, the only certain win is in West Virginia, where Huckabee won the state's 18 Republican delegates.
The delegate count is key when looking at the results. Candidates need to notch up enough delegates -- rather than voter numbers -- to secure their party's nomination.
More than four-fifths of the 2,025 delegates needed to clinch the Democratic presidential nomination and more than 1,000 of the 1,191 necessary delegates on the Republican side are at stake.
This year's presidential race is generating more interest than usual because Republican George W. Bush is ineligible to stand, while vice-president Dick Cheney is not running. None of the presidential hopefuls has been their party's official nominated candidate before. See which states are the most important. »
While last-minute polls on the Republican race indicated Romney has gained ground against McCain in California, Romney was expected to split races with Huckabee in the South, Republican strategist John Feehery said.
Huckabee announced Tuesday evening his intention to stay in the Republican fight: "As long as there are votes and delegates to be won there is one guy answering the bell every time there's a new round," he said.
Romney told his supporters: We are going to win this thing and go all the way to the White House."
Early Tuesday Romney and McCain, who have bitterly attacked each other's conservative records, evoked the spirit of two-time Republican president Ronald Reagan.
McCain, out on the streets of Manhattan with former New York City Mayor Rudy Guiliani -- who is backing him after dropping out of the Republican race last week -- said he is the Republican who can win the White House by gaining the support of independent voters. Watch McCain at a New York rally. »
He added: "We are the greatest nation on earth. We will continue to lead and we will be, as Ronald Reagan said, a shining city on a hill."
The final Republican candidate, Ron Paul, who has described himself as "the most conservative member of Congress" said Tuesday he would put the U.S. back on track with balanced budgets, elimination of income taxes and withdrawal from "entangling alliances," including the United Nations.
Obama Tuesday promoted his health insurance proposal, arguing that most people will opt for coverage if it is made affordable. Watch Obama's plans if he's elected. »
He told CNN's "American Morning" from San Francisco: "I am confident that if people have a chance to buy high-quality health care that is affordable, they will do so," Obama said.
Clinton cast her vote in the New York's Democratic presidential primary Tuesday morning at an elementary school polling station with her husband and daughter. Watch Clinton cast her ballot. »
She has campaigned on the contention that her eight years as first lady and Senate experience makes her more qualified than Obama, who has been a U.S. senator for just four years.
"The stakes are huge for our country, a lot of big challenges, but America's up to it," Clinton said Tuesday. "We just need a president who's ready on day one to turn the economy around and become commander in chief and get our country back on the right track." Watch the Democrats' differences on healthcare. »
Democratic Party Chairman Howard Dean told CNN "I dare say this is not going to be over certainly tonight, and maybe not for a month from now." E-mail to a friend