The demonstrations began last week at Johannesburg's prestigious University of the Witwatersrand, and have since spread to at least 10 universities, forcing the closure of many of them.
On at least two occasions, police foiled attempts by the protesters to reach the headquarters of the governing African National Congress (ANC), pushing them back to their campuses. But the students regrouped and finally reached the building, named Luthuli House after South Africa's first Nobel Peace Prize laureate Albert Luthuli.
The students sang and chanted anti-apartheid songs, invoking memories of the decades-long campaign which led to the overthrow of the apartheid regime in 1994.
The ANC pulled out its election truck and seemed to be wiring a loud speaker, but the students refused to let the party's secretary-general Gwede Mantashe address them.
Instead, they gave him a memorandum outlining their demands.
"The honeymoon of 1994 - when we were told that we were free - is over," a student leader said in his address to the protesters.
Students said they would march on Friday to government buildings in the capital, Pretoria, to coincide with President Jacob Zuma's plan to meet protest leaders to discuss their grievances.
The mainly black students say they cannot afford fee increases and have rejected a government offer to cap increases at 6%, down from the 10% to 12% proposed by the management of universities.
The 29 people who appeared in court in Cape Town were not asked to plead.
The accused have been released from police custody, and the case postponed to February.
Those charged include the 63-year-old parent of a student at the University of Cape Town, the privately owned News24 site reports.
It published what was purportedly an official document, showing "high treason" was among the alleged offences for which he had been detained. However, the charge was not mentioned in court.
Correspondents say the protests show growing disillusionment with the ANC, which took power after minority rule ended in 1994, over high levels of poverty, unemployment and corruption in government.
Many black students say they come from poor families, and fee increases will rob them of the opportunity to continue studying.
Financially better-off white students have joined the protest, mainly to show solidarity with the black students.
In a statement, Mr Zuma said: "It is important that we work together to find solutions. Nobody disagrees with the message that students from poor households are facing financial difficulties and possible exclusion."
Correspondents say his intervention shows how seriously he is taking the protests.
Students are also demanding the resignation of Higher Education Minister Blade Nzimande, who said on Monday that the protests were not a national crisis.