Another common circumstance is when a student attends an open house, or takes a formal tour of the campus. Many colleges offer free applications as a "thank you" for visiting. That makes good sense too. It's much easier to fall in love with a college while standing on the quad on a brisk October day than it is by means of printed or online materials (It took me exactly one Ithaca sunset to know I loved Cornell).
Another reason you may get to apply for free is if you're being recruited. Again, it's all about getting you to think of the college as "your" college, and recruiters know that's easier when you have an acceptance letter in your hand.
None of these compare to my favorite though--fee waivers. The short version is this: if you get a free or reduced price school lunch, you may be eligible for up to 4 free college applications. Check out this quote from CollegeBoard, then follow this link or talk to your school counselor for more information.
"If you've participated in the College Board's SAT Program Fee-Waiver Service, you may also be eligible to waive application fees at the colleges to which you're applying. Follow the link below to see a list of colleges that do not charge an application fee or will consider waiving the fee if you've received an SAT Program fee waiver."
PS A big shout out and THANK YOU to Ms. Small for help with this post!