I like to know my average speed just to guage my fitness level, right now, it ain't that good.
The other stats I have on the bike with a computer are fun to see, like max speed, and ride time, but I don't track them.
On of the most freeing ride was a few months ago, when I got a single speed 29'r. No computer, no gears to shift, just riding, and (this will sound corny) being one with the bike. It was a sublime enjoyment.