I am surprised that you guys don't consider the newer generations. For me at least Omega Ruby is my favorite, it used to be Sapphire but yeah. After all I prefer the new things like physical/special attacks and the choice of pokemon you have.
Definitely Pokemon Puzzle League. Pokemon Snap was also great. From the handheld-editions I find it difficult to favor specific ones. Probably Crystal? I really like the new combatsystem from Gen 4+5 but in terms of the amount of Pokemon it starts to become too much (and I despise the mega-evolution concept) and Crystal was superb with that multiregion-approach. That being said, I never got to play the remakes of the 2nd Gen so I might like those even more. The more defensive metagame in the first 3 gens also appears more attractive to me when looking at competitive.
White 2 and HeartGold ~ I prefer HG/SS rather G/S/C because there is a better version of BGM of Route 201 than in D/P/Pt xD Also the GB player in HG/SS is quite good as it contains some 8-bit BGM even if it didn't appear in gen-2 games. I personally do not like OR/AS :/
Pokemon Diamond and Pearl. Probably because that was my first. The funny thing is that I didn't even realize that there were games and I thought that it was just a TV show and when I saw Diamond on the store shelf for the first time I thought to myself, "Wait, they made Pokémon into a game?! I need it!!!" Replayed it last year and it brought back a lot of old memories.