1st - Generation 5
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Yeah, generally speaking it has the most Pokemon that I hate/don't care about, but game wise, it has to be the best by far. The entire region is incredible to explore, and all the little extra parts and details don't feel tacked on like they did in previous games.
I liked the way they cut down the legendaries, compared to the insane amount of useless ones in Gen 4, and made them all interesting and, most importantly, usable.
In every other Generation, the more titular legendaries have usually been one of these:
1) Caught post-game, making them rather useless.
2) Been legendary beings, which when caught felt like you were merely imprisoning them.
3) A danger to the region/world which is caught to tame its power.
In Black and White, this is different. Reshiram and Zekrom are powerful, sure, but they are never described as being wild, or dangerous, etc etc.
The one on your box art in fact chooses you as its champion, which I found awesome! No longer would I have another overpowered monster to be caged in my boxes, but a legitimate Pokemon to use! Another neat fact was the opposite chose N as its champion, making for an epic final rival battle.
The same applies for the legendary trio, the Musketeers. By the first/story ending of the game, the average trainer level of Pokemon is significantly higher than any of the trio, making them as legitimate to use as any of your other team.
The story was also incredible.
However the best thing, I think, is the post-game. A whole quarter of the region is opened to you, and while it has no Gyms, it has new Pokemon, trainers, and all sorts of things to do. Especially amazing was the Elite Four happening twice, which makes sense in the story. They are much tougher to finally beat than any other game, with the lowest Pokemon they have at level 71. Bearing in mind that the wild Pokemon you can fight to train your own cut short at 65 at best, training your final team up to a level that stands a chance against the Elite Four is a real challenge.
I still have yet to beat them, and I'm on my 125th hour.
So, in my opinion, while it does have the most sucky Pokemon, the rest of the game more than makes up for it.
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2nd: Generation 3. I really can't be bothered to explain it all, I just liked it the most. Has the best Pokemon for me. I also have a Flygon and Gorebyss that I've had for literally 9 years, so it really has been the game I've grown up with more than Gens 1 and 2.
3rd: Generation 2. Blah blah blah, improved on everything that happened in Gen 1, awesome Pokemon, blah blah blah childhood, blah blah blah two regions.
4th: Generation 1: Blah Blah Blah original.
5th Generation 5: It's last because it felt too forced for me. The Pokemon are badass to be sure, but the region was rather dull, the story was what we've all seen before and felt like Gen 3 in a different colour. It was just the least memorable and interesting game for me overall.
As a side note, I hope they stop doing remakes. I want a Gen 3 SEQUEL instead. Same region, same pokes, new story, characters etc though. Maybe a new city or two, and the possibility of exploring another region, maybe Sinnoh or Kanto?