assassinated dictator Park Chung-Hee, and her liberal rival Moon Jae-In, the son of North Korean refugees.
Opinion polls indicate the result could go either way.
The eventual occupant of the presidential Blue House will have to deal with a belligerent North Korea, a slowing economy and soaring welfare costs in one of the world's most rapidly ageing societies.
Park, 60, was looking to make history by becoming the first female president of a still male-dominated nation, and the first to be related to a former leader.
Her father remains one of modern Korea's most polarising figures -- admired for dragging the country out of poverty and reviled for his ruthless suppression of dissent during 18 years of military rule.
He was shot dead by his spy chief in 1979. Park's mother had been killed five years earlier by a pro-North Korea gunman aiming for her father.
Moon, who was chief of staff to the late left-wing president Roh Moo-Hyun, is a former human rights lawyer who was once jailed for protesting against the Park Chung-Hee regime.
Polling booths opened at 6:00 am (2100 GMT Tuesday) on a bright, chilly winter's morning, with the temperature hovering around -10 Celsius (14 Fahrenheit).
Initial turnout among the 40 million-plus registered voters was strong, with 35 percent having cast their votes by midday -- a sharp increase on the 2007 election.
"It's freezing cold, but I plead with the people to come out and vote to open a new era for this country," Park, wrapped up in a long coat and red scarf, said as she cast her ballot in Seoul.
After locking in the support of their respective conservative and liberal bases, the two candidates put a lot of campaign effort into wooing crucial centrist voters, resulting in significant policy overlap.
Both have talked of "economic democratisation" -- a campaign buzzword about reducing the social disparities caused by rapid economic growth -- and promised to create new jobs and increase welfare spending.
Moon has been more aggressive than Park in his proposals for reining in the power of the giant family-run conglomerates, or "chaebol" that dominate the economy.
"This is the only way for the people to change the world," Moon said as he voted in the southern city of Busan.
"This election is about our livelihoods, economic democracy, welfare and peace on the Korean peninsula," he added.
While both have signalled a desire for greater engagement with Pyongyang, Park's approach is far more cautious than Moon's promise to resume aid without preconditions and seek an early summit with North Korean leader Kim Jong-Un.
Although North Korea has not been a major campaign issue, its long-range rocket launch last week -- seen by critics as a disguised ballistic missile test -- was a reminder of the unpredictable threat from across the border.
The never-married Park has promised a strong, parental style of leadership that would steer the country through the challenges of global economic troubles.
"Like a mother who dedicates her life to her family, I will become the president who takes care of the lives of each one of you," Park said in her last televised news conference on Tuesday.
A female president would be a big change for a country that the World Economic Forum recently ranked 108th out of 135 countries in terms of gender equality -- one place below the United Arab Emirates and just above Kuwait.
Older Koreans, who generally favour Park, are seen as more dependable voters and Moon's camp has pushed hard to ensure the younger demographic that make up his support base cast their ballots.
One early voter, Kim Su-Eun, 29, said she had opted for the ruling party candidate.
"I think Moon's election promises are too radical while Park says she will carry out reform step by step. That's why I voted for her", she told AFP.