Red and Blue rescue team. Really liked to pair up with Bulbasaur because the powder moves were so useful when battling bosses. Also, Skitty/Delcatty because double-slap, for some bizarre reason, counted every hit as a full power hit, not a fifth.
My personal favorite is the Super partner. They have a really nice character arc and even surpass the main character in importance to the plot during the post game. And we of course mustn't forget the ending twist.
I like how the Gates to Infinity partner actually cares about the protagonist's life in the human world and tries their best to respect that they can't always be together with them. The other partners almost feel a little possessive in comparison.
The partner character in Super Mystery Dungeon actually had some nice moments I think. It's been a while since I played the game but I know they've had just as strong if not slightly stronger moments than even Explorers of Sky (and EoS is my favourite Mystery Dungeon game, by the way).