When I first purchased my first .357 I kept up with it by the boxes full of empty cases because I knew I was going to start reloading.
When I started reloading for a while I could keep up with it by either the receipts or the empty primer boxes, until I moved and didn't have the space to keep the empty primer boxes. I started reloading for a friend and acquired other .38 / .357s and then I could only keep track of how many reloads.
Later when I got my first .308 I kept up with my shots by the empty plastic .308 bullet boxes + 80 (The 4 boxes of factory ammo purchased), then I started being Mr. Nice guy and loaded up some of my bullets for some friends so the count I have now is off by somewhere between 100 and 200 rounds since I never kept up with how many rounds I reloaded for others. I do have an accurate count as to how many shells I have reloaded though not very useful unless Lee Precisions sends me a survey and wants to know....
The only Log type of thing I've ever managed to keep up with have been the little notebooks I've kept in all my vehicles since the first one where I log the Date/mileage / trip reading/gallons/cost of every fillup. Also use the same notebook to log oil changes, Tire / Battery purchases.
Until sometime in the future should I have the luxury of getting something in .22-250 or other caliber that is known to have a somewhat limited shot life then I might come up with a system for counting rounds through a firearm.
I think I can still tell you how many 25 pound bags of shot I've loaded for my 12 gauge shotguns since I was in highschool believe I still have all those neat cloth bags. I ran across 9 of them the other night, and have another stash in an old trunk. But that system won' work for long - recently I noticed that lots of places have downsized to 10 pound bags.