Opposition MSPs argue that funding cuts to the further education budget have forced colleges to reject suitable applicants because they cannot fund enough places to meet demand.
Information obtained from individual colleges by the Liberal Democrats showed colleges in the city rejecting more than 30,000 applications with thousands more put on waiting lists.
Stow College in the city centre had the highest number of suitable applications turned away, with more than 17,000 unable to be given a place in the last three years.
Others who said they could not accommodate all requests were Langside, Anniesland, City of Glasgow, Metropolitan, North Glasgow and John Wheatley College.
Glasgow Metropolitan, which merged into the City of Glasgow College, said it had a waiting list, which could be interpreted as the number failing to get a place.
In 2010, before the merger, there were 4908 people on the list.
City of Glasgow College said it had 8021 applicants on a waiting list in the last year .The previous year the figure was 2951 with 2128 applicants were on a reserve list.
The LibDems blamed college budget cuts and questioned the series of college mergers which they fear is increasing waiting lists.
Education spokesman Liam McArthur MSP said: "The Education Secretary needs to think again on his planned college cuts. These figures show colleges are being forced to turn away applicants due to a lack of places.
"How can the SNP Government seriously expect to tackle unemployment if it is slashing over £30 million out of college budgets?
"Those who attend colleges often face different circumstances than university applicants.
"They tend to look for courses on their doorstep and family commitments may mean they cannot relocate to another city.
"What happens when there's no room at their local college? These figures show that the SNP's decision to cut college budgets could have serious ramifications to the lives of our aspiring learners.
"Interestingly, our figures also show that applicants may also be languishing on waiting lists.
"City of Glasgow College had 8021 applicants on waiting list this year alone.
"I hope that the college waiting list audit can shed some light on this, but it is clear that there are questions to be answered about whether this really is best practice.
"I remain concerned about the pace and extent of college mergers being demanded by the Education Secretary.
"These figures demonstrate a need to review access and seek to widen it across both further and higher education sectors."
By STEWART PATERSON Political Correspondent