Do extra principle mortgage payments decrease the interest paid on the original loan, or do they simple decrease the number of payments made. I have a 15 year mortgage with 13 years left, and wonder about refinancing with a lower rate or just paying extra principle.

Extra principal payments reduce the amount of principal outstanding, which has the effect of (a) having les of your future payments go to paying interest, and hence more go to principal, and (b) shortening the time it takes to pay back the loan. So to answer your question - yes it reduces the total amount of interest you pay over the life of the loan and yes it decreases the number of payments you have to make over the life of the loan. What it doesn't do is reduce the amount of your monthly payment - it stays constant. You present your scenario as "either-or": either you will refinance or you will pay off some principal - but why not do both? Given the choice, I would suggest refinancing, as the reduction in interest payments goes right to your pocket, which in turn will make it easier to prepay principal down the road.