AP: Rival kid system.
AP: Their entire child system. I loved being able to have two kids and getting to actually watch them grow up made me want to keep on playing even well past Year 3. Only change I'd make is to slow the entire process down a bit. It takes half a season to finish a pregnancy in this game and barely longer for the kids to age.
Save the Homeland: The ability to chose different varieties of horses. AP did this as well to some extent but I loved how I actually got my pick in this game.
AP: The phone was a life saver on festival days. Please bring it back.
AP: Their mining system was my favorite out of all HM titles. I know some people don't like having to dedicate 15 real world minutes to something like that but I vastly enjoyed it.
Tree of Tranquility/Save the Homeland/Trio: The part-time job system. It was a nice little way to improve your heart rankings with villagers and earn money in the early game.
AP: BRING BACK THE HARVEST KING.
AP: While the bells did get tedious I liked the overarching narrative and felt an active dislike going back to SoS:FOMT and finding the story even more gutted there than it had been initially. It got immensely boring for me...
SoS:FOMT: The vibrancy of the color palette they're using is something I desperately want going forward. It just makes the games feel so much warmer.
SoS:FOMT: Equal marriage is something I desperately want to be a recurring theme.
HM64: LET MY CHARACTER GET DRUNK AGAIN PLEASE.
Magical Melody/DS Remakes: Bring back a soft achievement system please. While the Sprites/Musical notes aren't to everyone's tastes I really liked having a secondary objective to running my farm. It was something, like children in AP, that could keep me playing long after my farm goals and been achieved.
AWL: The seed maker. That's pretty much it as this is probably my least favorite game style in the series.
AP: Being able to have lots of pets and being able to teach them tricks.
Magical Melody: Pick where your first house is, then have the ability to buy other plots for farming around the entire map.
Magical Melody: Have horses be actually worthwhile beyond transportation. I made a pretty penny in this game just breeding and training horses for the big Horse Race festival, as any horse sold that had won it was worth A LOT.
ANB: I second the placement grid, as well as their entire building system. I don't want to have to build the entire town layout again but I would love the ability to customize my farm.
Trio/AP: Fertilizer system.
Trio: Crop and animal system as well.
Trio/Most modern SoS games: Their cooking system. I prefer it when the game has more recipes to play around with, however I do wish they'd go back to the old style of being able to still cook recipes if you lucked into figuring out their ingredients even without the recipe on hand.
AP: The models, minus poor Owen and his bobblehead.
AP: The amount of dialogue people have to say is insane in this game. However it's heart system is arguably one of the worst in the series. So I'd take that from any modern HM game baring ANB.
Trio: Town ranks.
ANB: Their multiplayer was FUN, if also immensely broken. I'd still like to see it again for the giant animals that'd spawn.
AP: The ability to change the furniture placement in my house and pick out colors I liked.
ANB: For the housing interior variety. Trio for the outside style variety.
Trio: The amount of festivals, again to help spice up gameplay.
AP: For the fishing variety.
AP/SoS:FOMT: A time system that bridges between these two extremes (very long days versus very quick days) would be ideal for me. As FOMT went by a little too quickly for me while AP's days were so long your character can be finished with all their chores/mining/greeting/etc well before 17:00 and then just have nothing but free time.
SoS:FOMT: Time freezing in doors.
Later SoS Games: The character customization was amazing, and I really loved the variety of clothing I could make for my character to wear.
AP: The ability to go outside during a typhoon.