I can't single out a single best one, so I'll just give you my favorites from every game I've played.
FE1: Player Phase. It's just so catchy and iconic.
FE3: Advance. I just love the heady feeling of adventure I get from this track. One of my most favorite player phase themes
FE4: Girl of the Spirit Forest. Compared to all the heavy and serious player map themes in FE4, this one stands out to me because of how different it is from the rest. It's cheerful. Hopeful. Catchy as hell.
FE5: Adversity. I haven't even played FE5 yet, and I can already tell that this is a piece of music about overwhelming odds. You're completely surrounded. There's no way out. Will Leif be able to survive the oncoming onslaught?
FE6: When the Rush Comes. I love this theme. It gives you a feeling of "Oh man. I'm about to start this great adventure." This one wins over the FE7 version since I like how it sort of has a foreboding tone to it at around 0:48, something that I think FE7's version didn't do justice.
FE7: Destiny Enlaced by Fear. Definitely my favorite song out of all the GBA games. It still gives me chills listening to it. Compared to FE6's Final Chapter and FE8's (I can't even remember the title since the music was so boring), I feel that Destiny Enlaced by Fear was able to give the listener a sense of Finality to it along with the heavy feeling of uncertainty and fear. The final battle is about to happen, but it isn't all fun and games, you know. There's a very high chance that this will be the last time we ever see daylight.
FE8: The Prince's Despair. The theme song of a tragic villain. I just love the buildup to the main melody in the beginning of it.
FE9: Crimea Attacks! I'm not a huge fan of the Tellius series music at all, however I have to give it credit. Crime Attacks is a badass piece of music. The buildup at the beginning to the brass fanfare is absolutely superb. I also just love how it gives the feeling of reclamation and liberation. Taking back what's rightfully yours.
FE10: Haven't played througout all of FE10 yet to properly give it a favorite piece of music. Echoes of Daybreak is pretty awesome though.
FE11: Footsteps of Fate. A haunting piece of music. Its dark, foreboding, and epic tone gives the game itself a taste of things to come. The beginning of Marth's struggle.
FE12: One Carves a New History. I just love the hopeful vibe I get from it. A feeling of shaping the troubled world to your liking.
FE13: Id (Sorrow) The tone of the piece is absolutely crushing. Like Destiny Enlaced by Fear, it gives the listener a sense of uncertainty and fear. But most of all, I love how it gives the sense of hopelessness. What if time can't be changed? The world may be doomed from the start and there's nothing that we'll be able to do about it.
Birthright: Alight. This song is fucking AMAZING. It has an excellent composition of brass and Japanese instruments that I find to be incredibly unique. It's such a hopeful piece of music.
Conquest: No Justice. Once again, a beautiful and unique piece of music due to its composition. The bagpipes and the plucked string intruments providing the melody really gives me the sense of a fearsome army.
Revelation: Those Who Visit I absolutely LOVE the percussion in this piece. The single snare drum, the xylophone melody in the beginning...I absolutely adore this piece. The tone of it really gives you a sense building up a resistance. The preparation for a battle against an unknown evil.
Fates: Thorn in You (Roar). Criminally underrated. Since you're not in battle most of the time this music plays, you only have time to appreciate the lackluster version of the piece. Betrayal. Sorrow. Violence. The instrumentation and melody of this beautiful piece of music radiates these feelings. It has an amazing use of brass, woodwind, and string instruments. Imo, the greatest piece of music that Fire Emblem has to offer.