I keep multiple sets of records that could be called "logbooks"--and I have gradually pared those down.
To me, "what to log" depends on what I see as the goal or utility of keeping those records.
When I was a newer diver, my dives were very similar to each other: a boat somewhere with warm water, 45-60 minutes in the water, a 3mm wetsuit with X lbs. of lead, and somewhere between 60 and 100 or so feet maximum depth. I began to realize that a lot of what I was recording was the same on every dive. I didn't need that information. I realized that often the only thing dive operators of the type that I did my diving with wanted to know was how many dives I had done in total, and my interpretation of that was they wanted to know how many of those kinds of dives have I done. When they ask that question, they probably don't have in mind 20-ft dives in a pool, so I didn't log those--or at least not in this log book, as I'll explain in a moment.
No dive op or instructor has ever asked to see my log itself. There are really just a few bits of data I feel I really need to keep track of. The second-most common question I have been asked is when was my last dive. On rare occasion I have been asked what is my deepest dive to date. Also, for my own interest, I want to know roughly how many lifetime dives I have done. In addition, as a newer diver I experimented with gear configurations, exposure suits, etc., did not yet have an intuitive grasp of how much lead to use on the occasional dives with a thicker suit, so I recorded all that information for future reference, too. But the traditional per-dive data increasingly seemed pointless, so I stopped recording so much detail. Of course, with modern dive computers more data than one can ever need to know can be downloaded, so what I am referring to here is a traditional handwritten log.
As I alluded to above, I started keeping a separate log of "training/practice dives." This might include courses I take, along with time spent just practicing stuff--maybe in a pool, maybe a quarry, a spring, even some open water dives where the goal is to practice skills or check out gear. I keep track of progress I make on learning certain skills, what I had difficulty with that day, what I need to focus on next time, etc. This is great stuff to log--just not in the same log book in which I keep track of other dives.
As the years went by and I started taking more courses and doing more varied diving, I realized just how similar those kinds of "vacation dives" I described above were to each other, and I stopped keeping track of them individually. Instead, I now keep a spiral-bound notebook in which I write a broader overview of each "vacation diving trip." Maybe I'll write that I did four dives a day for five days, or something like that. Only for dives that really stand out do I mention them individually. I write notes of what I liked and disliked about the dive op, the boat, the reefs, etc. Things like water temperature and the critters or wrecks or whatever I saw on the dives. I might note the people I met on the trip. Basically, a mini trip report, with no fixed format, mainly for my own benefit, though sometimes it will form the basis for a trip report I write up in full and post somewhere like SB. Again, what I'm recording is the kind of information that I believe will be useful to me if I plan to take a trip to that destination again.
When I started cave diving, I kept a separate log for those dives, because the information I need to keep track of is somewhat specific to that type of diving. My cave diving log is organized not by date but by cave (though I also keep a simple chronological list of dives). I want to know how many of those kinds of dives I did. I could certainly see keeping the same sort of log for wreck diving. If I did a lot of local diving, where I visited the same sites over and over, I would log only the information that I believed would help me on future dives.
In summary, I keep track of only what I believe will be useful to know in the future, and what is useful to know may depend on the kind of dive.