hmm, oh how do i begin with listing all the features that i liked? i guess i will do so in generational order.
Gen 1 - RBY: while Red remains as my favorite version of Gen 1 (Red being my fave color) Yellow AKA Pikachu Edition had some really great features, it started with Following Pokemon (only Pikachu but this is still where the mechanic began, so i digress.) but there was also Pikachu inspired minigames, which i would love to see more Pokemon-centric Minigames, would give all the more reason to "Catch em All!"
Gen 2 - GSC: Breeding - of course it is overlooked as being a mechanic but it's become a crucial part of our metagame as soon as it's inception in Gen 2, we use it for Shiny Hunting and to breed Champions. another feature that is overlooked (and sometimes underappreciated...) is the Day to Night System that runs off an internal clock, now you had reasons to be on Morning, Noon and Night to catch more pokemon, see time related events and even Evolve pokemon.
Gen 3 - RSE: Contests - now while i cant say that everyone liked the notion of Pokemon Contests, but i very much enjoyed the concept, why i even got a Magikarp Lv30 to the Finals of the Cute Category, with Splash, Tackle, Flail and Bounce. i would love to get back into contests and earn medals to show off to my fellow Pokemaniacs.
Gen 4 - DPP: Mining and Secret Bases - both mechanics went hand in hand with each other in DPP, you could mine for shards and invade other players bases to take their flags, it was the closest that Pokemon has come to Capture the Flag in MP, perhaps we can see that happen again one day.
Gen 5 - B&W: Repel Refresh - while a small mechanic in itself, being able to use another repel after you finished the first one made keeping weak pokemon at bay, especially while hunting for the roaming legendaries.
Gen 6 - XY: Trainer Customization - i know some players didnt like that the default character was free to dress up as you please, but i feel that with MP becoming more and more a part of Pokemon in general, we need to play as ourselves, which Gen 6 offered and i support it being a permanent mechanic.
Gen 7 - SM: Poke Ride - no more HMs bogging down our teammates or limiting our teams outside of Gym Battles, sweet christmas that is something i find LONG overdue.
oh and any new Battle Types or Endgame mechanics is very much been welcome in my book, the Endgame is a big deal for me, and facing trainers in even more ways just keeps it interesting.