I admit I do look at stats, but not as much scores as my kill death ratio (I want to be efficient!) And when I play medic (my most played class) I look at my death/assists.
But sometimes scores and even KDRs can be decieving.
Take the poor, poor pyro. His job at the time? To compression blast stickies away from sentry and spy check, do you think he will get many points? No. But did he save your sentry, dispenser, and teleporter many times through many ubers by pushing them back and blasting stickies and stuff? Yes.
Just one example I can think of that shows that score isnt everything. As a medic I also look at how much I have healed in the game, if its not a lot, I start healing more people, heh.
Anyway, thats stats for me, if you were talking about HLstats, then sorry I am off topic haha.