Saw a rat once at The All-Star Music. It ran out in front of us while we were walking back to our room about midnight, out of a stand of bushes. We jumped and screamed because we were surprised, but then we just walked faster. We're from a big city, Philadelphia, where you can put saddles on the rats so it was no big deal.
After that trip, while on Disney transportation, looking in the trees I see many rat traps "hidden" under mulch or whatever. That fact that I've only seen the one in 20 years of vacationing at WDW always amazes me.