Man this is a tough one. Ok, so let me get my personal favorites out of the way:
Verdanturf Town - such a unique one off track that I absolutely love. As a kid I would often go to this area just to listen to the music.
The 3 Lakes of Sinnoh - a song that made me want to learn the piano. Also where the journey starts.
Eterna Forest - what I love about this track is that I remember reading the sign at the entrance as it read, "the place where time stands still." That always stuck with me. Maybe that is why I find this track nostalgic and melancholic.
Sky Tower - From Mystery Dungeon Red & Blue rescue team. The final dungeon of the main story. The stakes are high, but you're praying that you can save the world. It is also the last hurrah for the protagonist and partner pokemon, and the ending always brings me to tears. Perfect track for the game's final dungeon (story wise that is).
Gen 3 Elite Four theme - Something about those opening trumpets and the midi sounds coming from a Gameboy advance cartridge makes this more epic than it needed to be. As much as I love ORAS, I don't think it topples the original track. It's the elite four after all, and this track not only gets you hyped up but it is nerve racking if one of your pokemon faints.
Diving theme in Hoenn - Using HM Dive for the first time was an unbelievable experience. Felt so surreal and cozy even if you're near the bottom of the sea.
Flashback theme from Black and White 2 - I want to thank my brother for letting me borrow his DS to experience these cutscenes. The song that accompanies them is as beautiful as it sounds sad. Especially the scene where some of the Plasma grunts say they will follow N no matter what. That's true loyalty.
Driftveil City - makes me get up and dance all the time.
Parting ~ Farewell - I'm not spoiling this one, but it is from the first Mystery Dungeon game.
Cycling theme from gen 1 - something about it I really love. It is a simple loop but a catchy one.
Ultra Necrozma Battle - Shin Megami Tensei Pokemon edition. Fantastic. A banger for one of the toughest bosses in all of Pokemon.
Gen 5 Legendary theme - banger. No other words to describe it.
N's theme - Both his battle theme and final battle theme rock. Feels mysterious at first, but as the track goes on it sounds like determination.
All in all, I think my favorite themes come from the first Pokemon Mystery Dungeon, Red and Blue Rescue Team. It's not just the themes that play throughout the story, but even the friend areas have amazing themes that I cannot stop thinking about. Gen 5 is also up there with the best music in terms of bangers too