A B737-300 flight crew rejected their takeoff upon observing uncommanded changes in the stabilizer trim.

Narrative

I initiated the takeoff using standard procedures; not doing anything out of the ordinary. Shortly after starting the roll; I felt a click of the [stabilizer] trim and didn't think anything of it; assuming one of us unintentionally hit a trim switch. After the 80 KTS call; I noticed another click of trim; and then another. I confirmed that neither one of my hands was touching the trim and looked at the Captain to ensure he was not inputting anything. The Captain and I confirmed what we were both seeing. He immediately took the controls and rejected the takeoff. I ensured the rejected takeoff procedures were followed; notified the Tower; and we taxied clear. The trim at that time was 0. We estimated the rejected takeoff speed to be approximately 110 KTS so we ran the brake temperature calculations; notified Maintenance; and returned to the gate. I heard rumors that this may have been caused by autopilot engagement; but I can ensure anyone that neither the Captain nor I reached up and physically moved the autopilot switches. I can't think of anything we did out of the norm to cause this.The only thing I can think of is perhaps practicing rejected takeoffs using other malfunctions than the usual ones; particularly at high speeds. I'm very self-critical and am sincerely open to suggestions as to what we did wrong or could have done better.