Some are having to reject budding students for the first time, with many institutions turning away four times as many applicants as the previous year.
Liberal Democrat leader Tavish Scott is calling for government action in next week's Budget to increase the number of college places.
He told MSPs during First Minister's Questions: "There has been a dramatic increase this year in the amount of people turned away from Scotland's colleges because there aren't enough places."
There was an 800 per cent increase in applicants turned away from Carnegie College in Dunfermline because courses were full, he said.
In 2008, 120 applicants were rejected, and this rose to 904 rejections last year, according to figures obtained by the Lib Dems.
Angus College in Arbroath, North Highland College in Thurso and Barony College in Dumfries turned away students for the first time because of capacity limits.