I never really played Pokemon until Gen III (though I was a big fan of the anime). That's always been my favourite generation. Particularly the introduction of Abilities, and in Emerald, the animated sprites. I know Crystal has animated sprites, but Emerald took them to a whole new level.
I also like Gen IV, but mainly Platinum and HeartGold. Just for the fact Platinum has more to do with Giratina, and HG/SS, you can walk with your pokemon. A pity Nintendo didn't implement that into B/W.
1st: Gen III
2nd: Gen II
3rd: Gen IV
4th: Gen I/V (I've not really played either... Gen I is a lot more difficult, while Gen V is just weird)
I love the anime, and have actually watched the whole Indigo League season (for the first time since I was like, 6.) in this past week, and I'm almost through Orange Islands season. But anyway, I don't go by Generations for favorites, but rather by the gameplay, Pokemon style, and character story, as a whole, which means the Versions. My favorites go:
1: Can never decide between Yellow and Crystal, while Crystal implements moving sprites, it doesn't have a Pikachu that enables you to get all starting Pokemon.
2: Gold and Silver bring up the rear, especially Gold. Ho-Oh FTW!
3: Emerald: It does an amazing combining of the two games before. Hoenn is in all three, of course, but it broadens the region. One way it does this is with the capturing of Groudon and Kyogre.
4: Of course, Sapphire and Ruby follow up Emerald.
5:Red and Blue didn't spark me like Yellow did, but I still enjoyed them.
6: Hmmm... So far, I have to say that Platinum is just okay... Too flashy for my taste, call me nostalgic, but the gameplay is just too animated. It slows the game down like CRAZY. It takes as much time to complete a catch on Yellow, than it does to actually throw the freaking Pokeball on Platinum! The Pokemon aren't anything remarkable, and it makes me miss the old games that much more, but overall, I give it a 2 out of 5, for the flashiness and Pokemon style... And also because they evolved Rhydon... :''''[ (Or is that in Black and White...?) Oh, and Lucario is awesome, I must admit.
7: Haven't played Black or White, but I have researched the Pokemon. Genosect is kind of a disgrace... The Legendaries aren't atrocious and the Pokemon are getting some of their old style back, but it is still a big stretch from matching Generation I, in my opinion. I give it a 3 out of 5, and when I play it, if it takes 20 seconds to catch a Pokemon, it will drop to 2.
So I guess the basic theme of things, from what I have seen with these responses, it really just matters when you started... If you started off with Generation III, you are bound to love that and forward, and if you started off at Generation I that will most likely be your favorite. I'm not saying that's how it is with everyone, just saying that's the information I have gathered here. On a personal note, I agree with Kirbychu all the way, not just because I started with Generation I, but because I enjoy the style. And THAT, my friends, is my general consensus.
P.S.: I have never heard if Generation I being difficult! O.o I think Generation IV is quite difficult, while I can complete Yellow in one sitting.