Dictionaries define "fare" as the cost of transportation, on a bus, plane, or train or in a taxi, for example.
A "fee" is the amount paid for a professional service.
Here are definitions from the American Heritage Dictionary*:
fare: 1. A transportation charge, as for a bus.
fee: 1. A fixed sum charged, as by an institution or by law, for a privilege: a license fee; tuition fees. 2. A charge for professional services: a surgeon's fee.
I can't think of any examples in which "fee" and "fare" would be interchangeable. Perhaps some of our users can?
Interestingly, the two words have different derivations. "Fare" derives from Old English "faer," meaning traveling, a journey or expedition. "Fee" comes from a variant of Old French "feu," which referred to an estate of land usually held in return for feudal service.**
* The American Heritage Dictionary of the English Language, Fourth Edition Houghton Mifflin Company 2003
**The Oxford Dictionary of Word Histories. Oxford University Press. 2002