I am looking at purchasing a single family home (4 bedrooms) near a local university.    It is zoned specifically "Single Family Home"   According to the zoning ordinance this means :   

Family means a person living alone in a single dwelling unit or two or more persons whose domestic relationship is of a continuing, nontransient character and who reside together as a single housekeeping unit in one dwelling unit. "Family" does not include a collective number of individuals occupying a motel, fraternity, sorority, society, club, boarding or lodging house, or any other collective number of individuals whose domestic relationship is of a transient or seasonal nature.

Should I be concerned about possibly renting to 4 unrelated students...  It seems to me this is a common occurance...   but legally I could get called out on this???

Here in Cedar Rapids, a SFM can not have more than 5 occupants that are unrelated.  You should obviously check with the your local authorities.  If your student tenants draw too much attention to themselves you want to make sure you are following the local ordinances.  My best guess if 4 will be fine.

Check the local zoning , this might not be all there is, you may fall under an area where the number of unrelated individuals living together is limited.  In some areas there is a specific ordinance prohibiting greater then x number of unrelated people living together.  In such areas this is targeted to control student rentals to a certain number of students. However these ordinances often use a reasonable number that your rental can accommodate but would not allow say a fraternity.  Check with the town and also look at the university off campus housing site to see if there is anything you might want to be aware of.  We have other student targeted laws in our area that it is good to know about before you are a landlord. 

We have a similar regulation in the 'burbs surrounding my alma mater.  None of the landlords followed the 3-4 unrelated person rule.  Six of us lived in one home (6 bedrooms), whereas the rules stated no more than 4. 

@Gary Fraser-Lee  what you posted would not allow for the living situation you proposed. Like others have said it happens all the time. That said, if push comes to shove you would knowingly be violating the local code and that would seriously jeopardize your position in court. Most likely nothing will ever come of it but that one time it does it will be painful. Proceed at your own peril. 

Thank you Bill.  What you say is exactly as I was thinking... most likely I would not have issues, but that one party (or whatever) with neighbors complaining to the city, could be all it would take for the city to start to question whether EVERYONE in the house was part of a "single family" or domestic relationship not seasonal in nature, as the ordinance states.     I have decided not to proceed for this and other reasons.