Abilities were one of the best things to ever happen to Pokemon. I never minded egg moves, loved double battles, and liked the berries, though I thought the item specific baby Pokemon was kind of stupid, especially since you couldn't access Gen's I and II anymore.
Oh, I forgot abilities came in Gen III, that was nice.
Egg moves were introduced in Gen II, and I have no problem with those, they make sense. What doesn't make sense is "know move X to get pokemon Y", it's the only thing IMO that makes as little sense as item-specific baby pokemon.
Double battles are Ok, but never really all there IMO.
Berries are great, but berries, like egg moves, were introduced in Gen II. What Gen III did was [censored] the berry system. Pick a berry and the plant dies? Please, show me a bush in reality where picking the berry causes the plant to die. It's so incredibly stupid, and growing berry plants is incredibly annoying. I'm hoping they do away with loamy soil from here on out. Berry plants shouldn't die when I take the berry. For the added bonus for those who want to plant berries, do what they did in HG/SS and allow us to carry a berry pot. That way getting berries isn't incredibly annoying and you can grow them if you want without having to remember to check on them all the time.
I hate the berry system since Gen II if you can't tell still.