Some see the run-on as a form of a fused sentence (one where two independent clauses have been joined together without the use either a conjunction or punctuation. Another form of the run-on is the comma splice (where a comma is used instead of a conjunction or the correct punctuation--often a semi-colon.)

I taught that a run-on sentence was one which went on forever. It may or may not be grammatically correct, but there were just too many parts to it...stream of consciousness.

Sometimes, a run-on sentence is exactly the right kind of sentence: I often use run-ons to show Lois's babbling.

The best run-on I ever read was in one of Yvonne Connell's works ( I think it was Discovery--the nfic version--) where Lois and Clark had this very long, passionate moment in one looonnnnggg sentence. The run-on was perfect timed and placed.

gerry