Conquest and every 4th gen game that's name doesn't begin with "R" (except the JP only ones) were the best games.
Diamond/Pearl: My first games and still my favorites, I will play them over Plat any day.
Platinum: Plat has 1 thing over DP, and it's the Battle Frontier.
HeartGold/SoulSilver: Hands down the best main series game. Every feature people liked in Plat (Frontier), none of the ones they didn't (Poketetch, Super Contests), and cool new ones like the Poketathalon and Pokewalker. Fight me.
PMD Explorers of Time/Darkness: Nope, not explaining why this is here. If you don't already know why, get off your ass and play the thing.
PMD Explorers of Sky: Improved version of the above. Recycling was nice, the bonus Shaymin mission was cute. Moving on.
Battle Revolution: I know this isn't showing up on anyone else's list, so hear me out. Imagine yourself as a 10 year old who loves playing Pokemon with his friends. The graphics in Gen 4 were... boring. However, when you could battle on that rich friend's huge flat screen television, battles became so much more interesting. So much fun, GF NEEDS to remake this ASAP
Pokepark Wii: Again, I was like 10 when this came out and it was fun as heck. Going around smacking people in the mouth with Iron Tail was super fun, and the games provided a bit of challenge, but not so much that it was unbearable. Except possibly the last Obstacle Hop. That was aids.
Conquest: I have played through the entire post-story of this game at least 4 times, and my current isn't even done yet and has over 150 hours logged. That's more than my copy of Black that I never reset has. It was such a huge break from the series that it made a huge impression. It managed to make a game where you played as a freaking warlord into a kid's game, something I assumed not possible. Best non Explorers Spin-off easily.
Games not on the above list that others have mentioned (or not)
Ranger & Sequels: HOW IS IT SO DAMN HARD TO DRAW A CIRCLE AUGHHHHH
The rest of the PMD series: Also very good, but generally topped by Explorers. You can't beat this game Nintendo, but please don't stop trying. PSMD was close, but it was a straight ripoff of Explorers and therefore gets no credit. Like, the void? Pokemon you think is evil is good and pokemon you think is good is evil? Are you even trying to be subtle here Nintendo?
Emerald: Still a very good game, but I can't stand anything prior to gen 4 because the Phys/Special split. And they don't have Gallade.
Anything older than Emerald: Haven't played it
Black/White 2: F I L L E R G E N. At least in BW I almost sympathized with Team Plasma. The PWT was fun, but Gen 5 as a whole was coming off the back of HGSS.
ORAS: Again, not as good as the point of comparison (HGSS). Delta Episode was incredibly unique though.
BEST OVERALL GAME:
Explorers of Sky and HeartGold/SoulSilver
Sky is just a shining example of what a Pokemon Spinoff should look and feel like. Riveting story, great gameplay, difficult but not grindy, very little cheese (*glares at G2I*), incredible post-game content (*glares at every game since Conquest*)... This game was a work of art, and it's story is the only game I cried over as a kid, except every time mom took my DS away :(. As I have said elsewhere, I still start to tear up when I hear "I Don't Want to Say Goodbye" or "Through the Sea of Time." 9.5/10, screw off IGN, you filthy haters.
HGSS took what has been described as "the perfect sequel" (GSC), and filled it to the brim with new features, updated graphics, and the like. 2 regions and the ability to rematch every GL topped it all off. The Poketathalon was the best thing to happen to the Pokemon series, and I still do pull out my HG game every so often just to screw around on that. The story was ass, but the originals gave it no support on that score. Also hit a far better difficulty curve then basically any other game, without too much spiking for bosses. 9/10, needs better story.