I thought it would be useful to provide a brief summary of notable changes this generation. However, I'll only list new/retconned abilities, changes to some gameplay mechanics, and new moves learned by old pokémon. For the base stat changes or new abilities/moves, you can check them on serebii.
But feel free to add things that I've missed on this list and are nevertheless noteworthy.
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OLD POKEMON WITH NEW ABILITIES now gains Slush Rush as one of its regular abilities
loses Levitate for Cursed Body
Entei = loses HA Flash Fire for HA Inner Focus (though currently unreleased)
Suicune = loses HA Water Absorb for HA Inner Focus (though currently unreleased)
Raikou = loses HA Volt Absorb for HA Inner Focus (though currently unreleased)
now gains Sand Stream as one of its regular abilities (Weak Armor --> Sand Stream)
now gains Drizzle as one of its regular abilities (Hydration --> Drizzle)
now gains Drought as one of its regular abilities
now gains Snow Warning as one of its regular abilities (Snow Cloak --> Snow Warning)
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OLD POKEMON WITH NEW MOVES learns Quiver Dance
learns Quiver Dance
learns Dragon Dance
learns Air Slash
learns Swords Dance & Jump Kick
learns Hurricane
learns Moonblast
learns Roost
learn Burn Up as an Egg Move
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CHANGES TO OLD MOVES/ABILITIES/MECHANICS-ate abilities (Pixilate, Aerilate) = x1.2 (from x1.3)
Dark Void = 50% accuracy, can now exclusively be used by Darkrai, fails when used by Smeargle
Ally Switch = +2 Priority (from +1)
Gale Wings = Priority Flying-type moves only take effect when at full health
Diamond Storm = 50% chance to raise defense by one stage AND 50% chance to raise defense by two stages
Leech Life = 80 BP (from 20)
Sucker Punch = 70 BP (from 80)
Mystical Fire = 75 BP (from 65)
Water Shuriken = Special (from Physical)
Burn (Scald/Will-O-Wisp) = does 6% damage
Mega Evolution = stat changes are immediately applied on the turn it mega evolves
(e.g. Beedrill gains the speed buff immediately after mega evolving, no need for Protect)
Pranskter = Prankster-boosted moves do not have an effect on Dark-type Pokémon, including moves called by Assist