I'm another in the paper log category. I do not have a computer convenient to the reloading bench so it is not convenient to log the information electronically.
I use loose leaf binders. I'm up to four--handgun cartridges, small bore rifle cartridges, large bore cartridges, and shot shells. The shot shell book also holds my inventory of blank log sheets.
Each cartridge gets its own tab. The main page logs the date, lot number, quantity, case, bullet, primer, powder and charge, COL, powder measure setting, and other remarks. Every reloading session is logged in the book no matter how large or small.
Since I do not do accuracy or velocity testing on every lot of reloads, I have separate sheets for that data. I use the lot number to reference between the main page and the auxiliary information pages. Also, I have sheets for notes and keep special information related to the cartridge in the appropriate cartridge tabs.
The log sheets were originally hand drawn but now I have CAD file versions and use a photo copier to make copies of them.
Lots of different methods and amount of information logged already posted. One is not better than any other, it is was the individual likes and meets his or her needs. The important thing is to log the information so it can be referenced again in the future.