I guess I don't think about it every day, though I know roughly how long it's been. Every now and again if I'm going to post, especially, I calculate it. Since I started on June 1, so far it hasn't been that hard and I've stopped counting in days but rather in months.
I do think it's useful in that when the little demon, the addict, the "mind parasite" as one book I read put it -- raises its voice, you have a big stack of progress you don't want to have to start over on. It helps you incorporate your pride into your resistance.
On the other hand (and PLEASE never use this as an excuse - that's the way to the slippery slope) -- if you fail one day you have not completely failed -- if -- and only if you move on from that day and double down on your determination to continue seriously to strive toward this lifestyle change. One psychological problem with counters (and this goes toward any kind of addiction, food, even) is that people think they've failed when they've stumbled and fallen once and they quit, rather than getting up and getting back on the horse to CONTINUE to ride toward the goal. They feel down, dejected, demoralized, and start thinking "why not?" The way to kick addiction is to stop the pattern and replace it with something else. "Why not?" just gives you an excuse to re-establish the pattern. If, instead, you can use your "counter" to measure the distance you've come without having slipped back into the pattern - the isolated stumble aside -- if you look at it that way, you can turn it back into a positive.