I once had a flap motor catch on fire while on a long final at PTK flying a rental 172. After a few seconds of disbelief, I called tower on the radio and told them I had a fire on my wing, most likely from a flap motor (flaps quit working, I noticed the flaps quit working, looked out and saw lots of smoke on my right wing). They immediately responded, "Do you want to declare an emergency?" I suppose I should have without hesitation said "yes", but I didn't. After a pause, I said "no". I wasn't afraid of declaring, I just didn't see how it helped my situation what so ever, and I had my hands full. I landed, turned right to the waiting fire trucks (I think those guys must sit waiting in their trucks, they got out there so fast), and pulled the mixture/switched off the mains.
Part of the problem of declaring, at least to me, is you have to "think about it", and sometimes in an emergency you are task saturated, and you don't have the mental reserve left to make a good decision.