Which older generations were the most influential?

Gen 2 had a lot of changes from the first, all of which are still used today.

- Introduction to Dark & Steel types
- Splitting Special into Special Attack and Special Defense
- Introduction to Items
- Introduction to hazards (Spikes)
- Shinies
- Friendship levels
- Breeding & Pokémon genders
- Playing as a female trainer (Crystal)
- Splitting your backpack into different sections, rather than having one long list of items
- Move Tutors (Crystal)

So, I would say Generation 2 was quite influential.

 

Gen I. It laid out the groundwork for every game since them.

 

Here I am, once again, changing my mind.
Gen 5.

Gen 5 introduced and helped improve old mechanics of the game. No more having to go into your bag for more repels, it will automatically ask you! Oh TMs never run out? New, awesome hidden abilities? Triple battles and Rotation battles? The music changing mid-battle?

Gen 5 is one of the most, if not the most, influential.

 

3rd generation. I love Emerald. Its my favourite game alongside Alpha Sapphire

 

Gen 2-3 are both some of the most game changing in both the game play wise and competitive wise, so i'd have to say those two probably