It is up to the individual to choose what to log. The question you need to ask yourself is why you are keeping a log. I stopped habitually logging dives a long time ago; I have enough logged dives to meet the requirements for most courses, and I am not interested in bragging about how many dives I have done, or how long I have spent underwater.
I do still have a log though, but I only tend to use it if there is something worth noting. This could be details of a specific site I may find useful in the future, or something like weighting for a different equipment configuration. Equipment checks seem like a worthy reason to me.
Numbers of dives, or bottom time isn't always important. I remember a particularly bad dive when I was a relatively new diver. I had about 40 dives at the time and had recently completed Rescue Diver. I was diving with two Divemaster trainees, both of whom were trying to notch up the 60 dives needed to be signed off. One was an aspiring stuntman (now working in the business), and the other an aspiring instructor. To get on the UK stunt register, you have to reach a certain standard in sports of your choosing, and DM ticks one of the boxes; he told me he would dive now and again for fun, but did not intend on working as a DM. I had dived with him before and always felt comfortable.
The other guy was a bit of an arse; he had a small number of dives more than me, but all in the same training quarry. His rush to be a pro rather than focus on his own diving skills worried me. When we discussed the plan, they wanted to kit up, jump in and dive for 20 minutes. They would then surface, float around for a bit, then do a second 'dive'.
I tried to talk them out of it, but for them it was all about getting the numbers. I made the point that as well as logging the number of times you have ascended and descended, you are also logging the number of times you have kitted and de-kitted, performed buddy checks, and entered and exited the water.
Their plan did not go as intended as the aspiring instructor's air consumption was horrendous; I also discovered he was not the diver he thought he was. Fortunately they canned the idea before we got in the water again. The second dive didn't last long - after little more than five minutes, he panicked and tried to bolt to the surface. At this point I had to take control and managed to calm him enough to make a normal, controlled ascent, and get him out of the water.
This dive did not meet the 20 minute rule that many seem to work to, but there was more stuff worthy of noting from that short dive than many long, incident free dives; what went wrong, how I dealt with it, what I learned, and most important - a note to give this guy a wide berth in future!