I should also imagine it would depend on which non-EU country you are from. Some countries have and easier ride with visas than others. This is advice given to US citizens by their State Department:
The Spanish Government scrutinizes visitors who overstay their visas or their visa-free entry per the Schengen Agreement. Immediate deportation after spending a number of days in jail is not uncommon. You should leave Spain promptly at the end of the 90-day visa-free travel period or at the end of the time stated on your visa.
So, 90 days without a visa but visa requirements after that period. They also recommend that you have 6 months left on your passport after leaving Spain although 90 days is the legal requirement.
These rules apply to most non-EU countries under the Schengen agreement.
If you go to this site and enter the country you are from and the country you are resident in, it gives the requirements for visas.