In Sims 1, you could homeschool kids from the bookcase and make more variety in types of families/stories because of that. I used to like playing around with making latchkey kids, orphan kids, Peter Pan stories, and the like. It was always a challenge to see how far you could get them.
I also liked so much that I could throw parties and teleport in as many sims as my computer would let me. It was my game, there were no limits, and the parties were so much fun. I used to like it when Drew Carey showed up because I could try to prank and torture him.
In Sims 2, I liked the gardening and seasons system better than any iteration. Gardening had good features like composting, and seasons were something my Sims had to plan ahead for if they were live-off-the land types. I miss the strategy and planning aspect that mirrors what we do in real life for things like that.
In Sims 3, the open world felt like an adventure. I loved always having lots of exploration to do on every map - it added to that sense of adventure. I also liked being able to play as a pet, follow them around the map and seeing the places they would go and the things they would do. Living vicariously as a pet was fun and always led to new discoveries that I didn't know about before. And somewhere, unfailingly, I could always catch Imogene Pelly's dog peeing on her foot.
One con of the earlier games that I'm glad we don't have to deal with is the no-shoes problem.
We can pick shoes for our outfits now, yay!