A Monitor report published in February called for the closure of acute services including the A&E department.
The trust that runs the hospital was put into administration by the health regulator Monitor on Monday.
Support Stafford Hospital campaigners and police said up to 30,000 people had joined the mile-long march, from the town centre to the hospital.
The campaign group said the town's Market Square was so full of protesters it took 45 minutes for it to clear after the march started at about 1400 BST.
Thousands of people had previously signed a petition calling for Stafford Hospital's services to remain and a campaign shop from the protest group has been set up in the town centre.
By Chris KingBBC Radio Stoke
For the past four years the name "Stafford Hospital" has been a byword for everything that is bad about the NHS.
Today, 30,000 people turned out with their banners and placards to send out the message that they believe their hospital is now safe, and they are prepared to fight for its future.
The special administrators were not there today but they will find it hard to ignore the views of so many people.
Last week they told me that they were starting with a blank sheet of paper when it came to the future of services at the Mid Staffordshire Trust. This afternoon the people of Stafford gave them a clear indication of what they'd like them to write on it.
Jean Tabarner, one of the marchers, said she had had cancer and that Stafford Hospital had saved her life.
She said: "We've got to try - if you don't try, no-one will listen. We've got to keep plugging away and hope that the administrators listen to what the people around here want."
Sue Hawkins, chair of the Support Stafford Hospital group, said she believed it was important for people to move on from what had happened in the past at the hospital.
She said: "We've got a safe hospital today and we're looking to the future."
She added: "We need to have an intensive care unit here, we need to have an accident and emergency 24 hours a day and we believe that's possible.
"We know there have to be changes, we know there may have to be some alliance with another hospital to achieve that."
Stafford Borough Council leader Mike Heenan, who joined the marchers, said: "The important thing is delivering services locally, for the local people.
"That's what we're fighting for - so that acute services can stay in Stafford."
Monitor has given the administrators for the Mid Staffordshire NHS Trust, Ernst and Young, 145 days to work with local healthcare organisations to produce a "sustainable plan" for the future of services at the Stafford and Cannock Chase hospitals.
The Contingency Planning Team (CPT) report to Monitor last month said staffing levels at the hospitals were not sufficient to meet required standards in the long term, given the current range of services and number of patients.
It said some services, including accident and emergency, intensive care and maternity, could be provided at the University Hospital of North Staffordshire, the Royal Wolverhampton Hospital Trust and Walsall Healthcare NHS Trust instead.
Unison officials said earlier this week the administrators had told the union that they "were not bound by the recommendations".
The town of Stafford has a population of about 63,000 people, while its surrounding borough is made up of 122,000 people.
The area covered by the health trust extends beyond that, also taking in homes covered by the Cannock Chase Council area.
Staffordshire Police said there was no trouble during the march.
Thousands of people have marched in opposition to plans to downgrade Stafford Hospital's services.