Run-on sentences are the opposite of sentence fragments. A run-on sentence has too many parts -- two or more independent clauses thrown together with no punctuation. Fix run-on sentences by rewriting or breaking them into two or more sentences:
Wrong: We have to fly to Providence then we will rent a car and drive to Newport where will we visit the Tennis Hall of Fame and tour the millionaires' mansions.
Right: We have to fly to Providence. We will rent a car there and drive to Newport, where we will visit the Tennis Hall of Fame and tour the millionaires' mansions.
A type of run-on sentence that is particularly easy to miss during proofreading is the comma splice -- two or more independent clauses put together with incorrect punctuation:
Wrong: Employees may use the executive cafeteria, they must bus their own dishes, however.
Right: Employees may use the executive cafeteria. They must bus their own dishes, however.