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>Gen 1
>Gen 2
>Gen 3
>Gen 4
>Gen 6
>Gen 5
Gen 1 being first is a given.
Gen 2 is probably one of the most important gens because it introduced: Breeding (let's be honest a lot of you autists spend time breeding pokes), Shinies (see above *breeding), SPECIAL DEFENSE (yeah your precious blissey and my precious milotic are different with the Special Defense stat), Steel and Dark, Gender, HELD ITEMS, weather, and a PLAYABLE female character.
Gen 3 is also important because it added things like: Natures (natures are an innovative and huge thing in the series), EV/IV system is another feature that is very important too, formes are important too because of forms we got mega evolutions (a special kind of form), some rebalancing to Pokemon such as Scizor
Gen IV added significantly less than the previous three generations but still added features that changed the core gameplay.
Special and Physical split is a critical feature that buffed a lot of Pokemon. Without it, Pokemon like Arcanine, Dragonite, etc. get a lot crappier because they can't put their Attack stat to good use. Wi-Fi is a major feature too because we wouldn't have been able to trade and battle amongst across the world
Gen VI added three new features that will change the series forever. One of the biggest is Mega evolutions. Mega evolutions are a temporary form in battle that buffs a lot of existing Pokemon and changes the way you make some teams. Fairy type is a new type (full of shit pokemon with a couple exceptions) that is immune to one of the best types in game. Types got "rebalanced" with steel now having neutral damage from dark and ghost types and some Pokemon got very slight buffs to their stats for the first time since G/S/C
Gen V is probably the least important generation in the series. It didn't add anything that changes CORE gameplay like other generations have but added small convenient things like: Infinite TMS, Repel asking you if you want to use it again, and different ablities.
Yep.