Should I put my wider tire in front or in back? My used bike came with a 700x28 tire in front and a 700x23 tire in back. Should I leave the wider tire in front, or should I switch the tires? What benefits or drawbacks are there one way or the other? Is there any particular reason why the previous owner might have chosen non-matching tires? Is there any reason I should go out of my way to buy a new tire to make them match?

The found a little bit of information about tire sizing, but I still don't feel like I know what to do.
Generally on a road bike it is considered better to run tires of equal size.

There are a few newer tires which are designed to run different sizes front and rear, but they are usually within 2 mm of each other. (Like the Continental Attack/Force combination)

I would consider a jump from 28c to 23c somewhat large.

That said, run the larger on the rear. The higher air volume will make for a more comfortable ride, and the narrower front tire will steer quicker, which makes for more reactive handling, and has a better aero profile, (which may or may not matter to you).

The comfort part will matter though, and I'd say that's a trump card.