I'm going to sound like an @ss or completely OCD here, and I apologize in advance. I'm meticulous about how my tires are installed. Many tires, both road and mountain, are directional, so there's that to consider. Depending on the tire and conditions, I may run my rear tire in the "reverse" direction, if I'm looking for extra traction. Sometimes, I'll run the rear tire in the "front" direction if I don't need all that traction and it improves speed/rolling resistance. Really depends on the tire though.

I also ensure that the tire label is directly over the valve stem hole in the rim. Having that reference point can be very helpful when you've punctured a tube and are trying to find the offending debris in the tire.

And yes, I've been known to dismount and re-mount a tire if I've screwed up either consideration...