It's very good to write your running log. It can be very helpful if you are seeking for results and set goals. It helps to find out problems if something bad happens. You should write these things about running every time:
But all the details you should write really depends on your goals. If you want to lose some weight, you should really write it everytime, if not - it's not necessary.
For example if you feel very bad after running, if you feel that it's getting harder to run every time, just look to your diary and try find out what did you do wrong. Maybe one day you ran to much, maybe you did too much running exercises. The same if you feel good. You just keep doing the same and maybe run longer and faster :) If you are willing to lose some weight, it's very good to write what you ate that day. If you see that it's goind down, that's wonderful. If you see that you weight more, maybe you should run a little bit more or eat less (especially candies, meat and fatty food). If you get to your wanted weight, you should write it every day too, because if something goes wrong (up or down), you should change something. So running training is really helpful in making future desicions about running training.