I can't really crown one as my favourite, but here is a list of ones I like:
Route 209 - I have only felt so much adventure in a Route theme before with Route 10 in BW. Honestly, it feels like I'm about to go trekking up a Welsh mountain with that intro (and yes, I do know what climbing up a Welsh mountain is like).
Mt Coronet upper floors - speaking of mountains, is it just me or is Mt Coronet one of the most majestic themes in all of Pokemon?
Battle Trainer - this theme is pretty good to start off with, but then reach the midsection and it suddenly becomes intense, with the tension increasing by the second. It's just epic.
Battle Barry - that start feels so happy, and almost makes me feel hopeful. Considering it's the first battle theme I heard in Platinum, it made me feel like I was going on an adventure!
Sunnyshore city - so happy! Also it's the location of Volkner, who is probably my favourite Sinnoh leader. And for some reason Jasmine is there, and she happens to be my favourite Johto leader!
Every Galactic battle theme - the hype of the grunt theme, the intensity of the commander theme and the sheer intimidation of Cyrus's theme. All three of them are epic.
Battle Lake Trio - the first Sinnoh theme I heard, seeing as heard it in Omega Ruby which was my first game. Back before I knew what mirage islands were, I went in blind and was intimidated as f**k by the opening, before bopping along to the rest.
Edit: crap! I forgot my HGSS picks!ill just list a few for now.
Route 47/48 - tbh this route theme is SO underrated. It feels so epic, and as it's beside a cliff it makes it feel even more awesome!
Kanto Wild Battle - head-boppable. Need I say more?
Kanto Trainer Battle - same as above.
Battle Lance/Red - god this feels epic. Tbh I prefer seeing this as Lance's theme since he is Johto's champion, but it doesn't change how climactic, intense and awesome the theme itself is.
Battle Rival - it's a super intense theme for a super intense guy. I mean, I did kinda ruin the moment for myself by naming him lmpp as an abbreviation for lamepoop, but who cares? The battle theme is so cool!