Okay, you're going to call me a crazy control freak, but that's fine, it's not like I don't already know...
I only really play one save, and to keep track of its population, I have a very big Excel file that lists all sims alphabetically by name, along with information about their gender, career, traits, etc. Here's an example, I split it in two screenshots to make it easier to read, but it's really one long row per sim.
https://abload.de/img/bonnie014xfvg.jpg
https://abload.de/img/bonnie020hio8.jpg
Explanation: Bonnie Bumblebee is a female human, young adult, lives in Brindleton Bay, is neither a celebrity nor a ghost, works as a an environmental manager, her traits are Childish, Geek, and Loves the Outdoors, no university degrees or club memberships at this time.
Since I play with ageing, free will and neighbourhood stories off, not much ever changes without my approval. When somebody does move, change jobs or occult status, I update their entry accordingly. Cats and dogs are also listed, but not small pets or farm animals. One thing I do not keep track of is aspirations and bonus traits because I change them on the fly. I also don't care about relationships, but there's a separate tab in this same file listing all the households and their members.
There's a reason I'm using numbers instead of X's or check marks for the species and gender entries. It's for the statistics at the bottom of the list. I only learned much later that Excel can also count words, not just numbers, which means this list could be a lot less bloated, but it is what it is now. And it will get even more bloated if my language (German) ever gets the pronoun update, because then I might add a third gender option. At the moment, sims with custom gender settings are categorised based on the pronoun the game uses for them.
The statistics also tell me how many sims and households live in each world (Newcrest is currently number one with 32 played residents, but San Myshuno has more households), and how many sims are in each age group (unsurprisingly, almost half of my played sims are young adults, and there are currently no toddlers in my world). Sooner or later I'll add career statistics as well because I'd like to see which ones I use the most.