There's actually a section in the TamaTalk lirbrary dedicated to keeping journal logs on your tamas. ^.^ I personally don't keep a log but a lot of others do.
I tried keeping a log of my Tamagotchis a long time ago, back in the days of the P1 and P2, but considering the fact that I am not very organized, I gave it up pretty fast. It is a good idea in order to learn "behavior" patterns, but I never seemed to log more than a day or so. heh I AM currently recording "special" events when I see them (such as Christmas tree visits and making faces)for different Tamagotchi so I can post them on the forums for people to see. That's about the best log I can do.