We keep 3 logs for our trawler. The "ship's log" is a hardbound book in which we hand record dates, times, events, engine hours, routes, destinations and interesting/unusual events and information (eg dock/fuel cost). It makes for interesting reading after a while. Always a good reference in terms of where to anchor/dock and distances etc. On overnight passages we record GPS positions hourly.
The other logs are computer data records. The Maintenance Log is a Word doc divided into sections by major boat part such as "Main Engine", "Generator", "Windlass", "Deck" etc. Here we record all activities involving maintenance or upgrades. For example, this record shows last time engine oil was changed by engine, or last time batteries were watered in chronological order. It is a perpetual record in that all activities from the date of buying the vessel are recorded.
Lastly, there is the "Spare Parts Log" that is a Excel file recording all identified parts by part number, source and last price paid for all routine replacements and any parts expected to need replacement in the future. This also logs all model and serial numbers etc for engines, generator, stabilizers etc.
There is no great complexity to the formats. They are just lists of events or parts.
The important thing is to keep track of what you have done, and when, and to try to make it easier to do the next time. Another "log" that we keep here in New England is a detailed list and set of procedures for winterizing and (my favorite) "summerizing" the boat.