Polls point to a very close race on Sunday between Ms Merkel’s centre-right Union bloc, with state governor Armin Laschet running for chancellor, and the centre-left Social Democrats, for whom outgoing finance minister and vice chancellor Olaf Scholz is seeking the top job.
Recent surveys show the Social Democrats marginally ahead.
The environmentalist Greens, with candidate Annalena Baerbock, are making their first run for the chancellery, and polls say they are several points behind in third place.
The Social Democrats have been boosted by Mr Scholz’s relative popularity after a long poll slump.
Ms Baerbock suffered from early gaffes and Mr Laschet, the governor of North Rhine-Westphalia state, has struggled to motivate his party’s traditional base.
About 60.4 million people in the nation of 83 million are eligible to elect the new Bundestag, or lower house of parliament, which will elect the next head of government.
No party is expected to come anywhere near an outright majority, with polls showing support for all of them below 30%.
Such a result could mean that many governing coalitions are mathematically possible, and trigger weeks or months of haggling to form a new government.
Until it is in place, Mrs Merkel will remain in office on a caretaker basis.
Mrs Merkel has won plaudits for steering Germany through several major crises.
The new chancellor will have to tend the recovery from the coronavirus pandemic, which Germany so far has weathered relatively well thanks to large rescue programmes that have incurred new debt.
Mr Laschet insists there should be no tax increases as Germany pulls out of the pandemic.
Mr Scholz and Ms Baerbock favour tax hikes for the richest Germans, and also back an increase in the minimum wage.
On Friday, Mr Scholz touted the outgoing government’s success in preserving jobs during the Covid-19 pandemic, declaring that “we are succeeding in avoiding the major economic and social crisis that otherwise would have hit us”.
“We will achieve new growth if we do the right thing now in economic policy,” Mr Laschet said at a rally on Saturday in his home city of Aachen.
“If we do it wrong now, with ideological experiments, everything that we have built up in 16 years will be squandered.”
Ms Merkel, making the last of only a handful of appearances in this campaign, praised Mr Laschet as someone who “builds bridges, takes people along with him”.
Germany’s leading parties have significant differences in their proposals for tackling climate change.
Mr Laschet’s Union bloc is pinning its hopes on technological solutions and a market-driven approach, while the Greens want to ramp up carbon prices and end the use of coal earlier than planned.
Mr Scholz has emphasised the need to protect jobs as Germany transitions to greener energy.
Foreign policy has not featured much in the campaign, though the Greens favour a tougher stance towards China and Russia.
As they have struggled in the polls, Mr Laschet and other Union leaders have warned that Mr Scholz and the Greens would form a coalition with the opposition Left Party, which opposes Nato and German military deployments abroad.
Whether such a partnership is realistic is questionable, given foreign policy and other differences between the parties, but that line of attack may help turn out the conservative base.
Mr Scholz has said he would like a two-party coalition with the Greens, but that looks very optimistic.
Absent a majority for that, his first choice would probably be an alliance with the Greens and the pro-business Free Democrats.
A coalition with those two parties is also Mr Laschet’s likeliest route to power.
The Greens favour an alliance with the Social Democrats, while the Free Democrats prefer one with the Union.
The result may also allow a repeat of the outgoing “grand coalition” of the traditional big parties, the Union and Social Democrats, under either Mr Scholz or Mr Laschet.
The far-right Alternative for Germany party is polling a little below the 12.6% it won to enter parliament in 2017, but will not feature in any new government this time either.
All other parties say they will not work with it.
The Bundestag has at least 598 seats, but Germany’s complex voting system means that it can be considerably larger.
The outgoing parliament had a record 709 seats and the new one is widely expected to be even bigger.
The number of people voting by postal ballot is expected to be higher than the 28.6% who did so four years ago.
Also on Sunday, voters in Berlin and in Mecklenburg-Western Pomerania in north-eastern Germany – both states currently led by the Social Democrats – are electing new state legislatures.