Our school has required reading logs since K, and DS8 is now in 3rd. I also have one just starting K. In K, they want 15 minutes daily of either a parent reading to the child or the child reading with supervision. The amount of reading time required has grown to 30 minutes over the years, now with fiction and non-fiction book reports due each month.
In our school it is mostly to make students and parents aware of how much reading is going on and to encourage more of it. The parents are required to sign the log, and at the end of each month the students who have every day filled out get a coupon for a free personal size pizza from Pizza Hut. My kids like to save up their coupons and "treat" the family to dinner every few months.
I also really like being able to look back and see what the older son has read over the years, and will probably hold on to it for quite some time. If nothing else, when we move this summer to a new school district it will help to illustrate his reading habits/abilities to a new group of educators.