The decades-old state of emergency law has been partially lifted to mark the anniversary.
Mr Mubarak is on trial accused of ordering the killing of demonstrators.
He denies the charges.
By Tuesday night, thousands of protesters had already gathered in Tahrir Square, the focus of last year's demonstrations. They were joined by thousands more in the morning.
The BBC's Jon Leyne, in Cairo, says the mood is peaceful so far, resembling more a huge street party than a political protest.
The various groups are all competing to claim ownership of the revolution, says our correspondent, from the youth movement which began the protests a year ago to the Muslim Brotherhood, which now dominates parliament, and the Supreme Council of the Armed Forces (Scaf), which took power last February after Mr Mubarak stepped down.
Protesters who stayed in the square overnight put up tents and chanted slogans against the military council, which many say should stand down immediately.
"The Egyptian army killed us in Tahrir and I am not afraid to say it," demonstrator Khaled Abdallah told the Reuters news agency.
"The army and police murdered us and cut off the revolution's voice; but I am telling you now, the revolution's voice will not be silenced," he said.
Other groups chanted "Down with military rule" and "Revolution until victory, revolution in all of Egypt's streets".
But some people in the square said the protests should end and the new leaders be given time to move Egypt forward.
"The council will leave power in any case. Sure, the revolution is incomplete, but it doesn't mean we should obstruct life," accountant Mohamed Othman told Reuters.
Others said they had turned out to remember those who lost their life in the uprising.
"We should not forget that there was bloodshed here. This is not a celebration, but it is a big event to send our condolences to our brothers who passed away between the 25th of last January and now," said Walid Saad.
On Tuesday, Scaf chairman Field Marshal Mohamed Hussein Tantawi said the state of emergency, which has been in place in Egypt almost continuously since 1967, was to be lifted.
But Field Marshall Tantawi said the law would still be applied in cases of "thuggery", without giving any details.
The military has used the term "thugs" to justify the crackdown on people demanding a return to civilian rule.
An end to the much-hated law had been a key demand of the protesters. During his nearly 30 years in power, Mr Mubarak had repeatedly promised to lift the decree and then failed to do so.
Last year, the generals widened the scope of the emergency law to include labour strikes, traffic disruption and spreading false information.
The newly elected parliament met for the first time on Monday since elections - which took place over several months - returned an Islamist majority.
The Freedom and Justice Party (FJP) of the Muslim Brotherhood - banned under Mr Mubarak - holds the largest number of seats.
The session began with a moment of silence for those killed in the anti-Mubarak protests.