Issues which drove them to the brink included sexual abuse, eating disorders, relationship problems and depression.
More than 1300 students from Glasgow University signed up to see a counsellor in the last academic year, a rise of 160% since 2008.
At the University of the West of Scotland (UWS), the number of students seeking help has risen by 112% in the same time period.
One student studying at UWS, which has campuses in Paisley, Ayr, Hamilton and Dumfries, turned to the university-run service for support when he was struggling to cope financially. having being made redundant shortly before starting his course.
The third-year student said: "Redundancy and the subsequent inability to get a job in the four months that followed left me feeling depressed.
"I also partly looked into counselling to help with my attitude towards money, and how having none was also leaving me feeling terrible, but this was, of course, because I didn't have full-time work."
Another postgraduate student said she needed help following a relationship breakdown at the start of her course. She said: "I was feeling overwhelmed and very down, and financial issues were a worry too.
"I didn't want to go and talk to my doctor, but I knew I wanted to get some sort of support to get me through a difficult time.
"I don't have that much money and wasn't able to pay for counselling myself, but knew the university offered me a free service for a short time, so decided to make use of that."
The recent economic downturn has left many students struggling to cope on their already squeezed budgets, which student representative Jessica McGrellis thinks may be a factor in the increasing numbers seeking counselling.
Jessica, who is the president of Glasgow University's Students' Representative Council, said: "I think a lot of students, particularly in the current economic climate, put a lot of pressure on themselves to do really well.
"It's not good enough to get just a degree, you have to get a really good degree and do a lot of other things as well.
"I think students are stretching themselves a lot but it's surprising that, since the economy has improved a bit recently, we haven't seen a decrease in the numbers going to counselling."
Glasgow Caledonian University has also seen a 27% increase in the number of students asking for help since 2010, the most recent year comparable figures were available.
The university has attributed the rise to a "number of factors including heightened visibility and awareness of the services offered".
A spokesman for Glasgow University said student welfare was one of the institutions highest priorities and added: "Whilst it is true there has been a rise in the number of students seeking assistance, this may - at least in part - be due to increased awareness of the services and support that is now available."
A University of the West of Scotland spokesman said the service provided, "valuable emotional and development support" for a wide range of complex issues.
Glasgow School of Art has seen a steady number of students attending its counselling service over the last five years, with an average of 163 students attending each year.
Strathclyde University's figures could not be compared due to a change in the structure of the service from 2010.