Hummmm, tough question really.
Seems I run a lot of different engines a little, but perhaps one of my many Jensen #25's or #75's may actually have gotten the most hours over the long haul as they tend to be go to engines for any accessory testing or quick steam fix. I have a handful of engines out and ready to be run, while most of my engines are actually put away in various storage scenarios, so don't see much action.
There for a while, and maybe still, the Chicken Barn Jensen #50 was being steamed more regularly than any other, and once fired up it tends to be run much longer as well, but it really doesn't meet the "my" engine specification, so I don't know if I can actually count it here.
I do have quite a few hours on my Solar Engines Sun Runner as well, but that is highly seasonal, and this isn't its best season, though it still romps well in mid-winter when given a good sunny day.