Unless I'm in a competition where it's required that I write down a score I don't.
After the round I replay the holes in my mind and write the score down. Usually I know where I stand in relation to par but it's one of those deals where I know but I don't know.
Even when I'm keeping a scorecard as I go all I really care about is my next shot and "the score" is only somewhere in the back of my mind and doesn't even matter.
I'm not very likely to break any personal scoring records anyway so all I'm doing is having fun, trying to figure out how to not make bogey, and seeing how many birdies I can make. One shot at a time and one hole at a time.
This is the best advice IMO. Since I started doing this a few months ago, my score has dropped 5 strokes due to me not putting pressure on my self to save par or whatever it is. If I am playing with someone, I let them keep score as just tell them what I made hole by hole (bogey, par, bogey, double, par, par, bogey, etc.). I don't count each stroke as I play the hole, and I don't look at the scorecard until I'm done. This really has helped me.