My favs in order from least favorite to favorite with a reason or two would be:
Gen2: I grew up with Diamond and Heartgold, and because HG/SS is just a remastered G/S/C, it's down here.
Gen3: I have fond memories of playing my cousin's Emerald and FireRed.
Gen5: White and Black2 were tied for my 2nd(now 3rd, I'll explain later) favorite Pokemon games because of all the fun new additions and beautiful asthetics(IMO).
Gen4: As I said before, I grew up with Diamond, my first ever game.....which I lost.....and HG, my personal 2nd favorite Pokemon game. HG's "walking with your Pokemon" feature made feel more connected to my Pokemon(also the s***ton of breeding I did)
Gen6: THE KING HAS ARRIVED! All the new features really keep me playing, my favorites being the Battle Chateau, Daycare, Pokemon-Amie, and the DRAMATICALLY improved online-multiplayer trading, etc. I'm with you, Gen6 is the best!
I honestly don't mind the show deviating from the games. I get the criticisms, but I like Ash's Pikachu. He probably just has really high IVs, and the first season nonsense of "aim for the horn!!" is long gone.
You can't cover that crap up with "high IVs," when the maximum is 31 and Pikachu is still practically useless even then. But hey, to each his own; you can have your non-canon Pikachu, and I'll stick to the source material, something the show could learn how to do.
I like to think of Ash's Pikachu as what a regular one would be like with a light ball. They really should have touched on what was unusual about him, at the very least. I'm fine with the non-canon one. The show could do a better job with that, but that's the last of my worries as far as it's concerned.