While looking at my bike a week or two ago, I noticed that there was a gouge in one section of the front tire. I told myself it needed to be replaced, but then one thing lead to another, and it was not replaced. I suspect I've put 3000 - 4000 miles on the tires, so it is not fair to complain that they may be a little worn.
While riding to work today I noticed a creepy little rhythmic bumping as the wheels turned. The rear tire had split and part of the tube is now visible.
Time to replace both tires...