I do keep an eye on my average speed and miles, also like to see what my avg. cadence is after my ride. I don't worry too much about time - my speed is slow-moderate - I just keep track of speed and cadence as a way to measure my improvement.

I also refuse to refer to my rides as "training", though they are - I have more fun when I think of them as "rides". It is a small distinction but it makes a difference for me as a relative newbie.