My most memorable sims is from TS2 and it's been maybe 15 years since I played her. Still remember her quite well.
She was part of my third generation, red head called Claire. She was quite ugly (ad a kid it was somehow really important how my sims looked like, killed many for their looks ?) so I had no high hopes or big plans for her. But she actually turned out to be one of the most interesting sims I had played, maybe because her story was something else than my normal "get a good job, find love, have kids, die".
She lived alone and tended her late grandmothers garden as a job and one evening a grey wolf came to visit her. They became friends and she adopted the wolf, called Nirri. She became a real wolf fan and spent rest of her life trying to become a werewolf. Easier said than done! I had her yard grow full of weeds and befriended every wolf I could find. Once it was sooo close, but I accidently cancelled a "bite" action of a wolf before I really realized what it was ?? She sadly never fulfilled her dream but she became one of my favorite sims ever.