Playing on your emotions is what the 5th Chapter does, and its theme, Door to Destiny doesn't hold back- you can feel the determination, the sorrow, and all of the emotion that the chapter has just by hearing it... and that's Not mentioning the arranged version.
May not be catchy, but if Yuria's Theme isn't moving, nothing is.
Fellow People, the recruitment theme. Though Fuuin no Tsurugi remixed it, the original version is still the best.
Light and Dark, the Chapter 10 theme. Celice is about to make his homecoming, but a few obstacles stand in his way — including the emperor himself — and this theme captures the atmosphere perfectly. The arranged version is even better. It's so awesome it was reused for Path of Radiance (see below).
Speaking of FE 6, after you've gone through some tough fights, Beneath A New Light plays, giving you the resolve to face on even greater challenges.
Victory from the first game, which has been remixed asA Knight's Oath in 6 and 7 and its FE 9 version Vow, usually accompanied by some awesome loyalty speeches. Also Unshakable Faith which helped create a CMOA in the final chapter of FE 7.
And the good guys aren't left out either. The heroes of FE7 get their own "epic boss music" - Blessing of the Eight Generals, which plays whenever a character is using one of the Legendary Weapons once wielded by the Eight Heroes. The song is slow, beautiful, sacred; not what one would expect of a weapon theme. However, considering that the theme's very name means that the greatest heroes who have ever lived have chosen to pass on their deeds and weapons to you and your companions, it's an extremely touching and powerful final battle song. And it's yours, for once, not the bad guy's!
shocking truth II, which plays when you find out Eliwood killed Ninian. Combined with the autoscrolling, unskippable text, it makes for the best cut scene out of all the Fire Emblem games, including the 3D ones.
And to twist the knife even further, if you got an A Support between Eliwood and Ninian before she is taken away, when Ninian speaks her last words, a new, unique theme, Shattered Life plays, as well as her speech changing to reflect the new mood. These changes ramp her death scene up from "Nergal, you bastard!" to near Tear Jerker levels.
The scene where Eliwood's father dies also gets suitably heartbreaking music, namely Final Farewell. Awesome enough in itself, but becomes almost a double Tear Jerker to those who've played FE 6 and remember the exact circumstances in which the original played.
From Sacred Stones, we have Land of Promise, played as you are about to face the Big Bad's Dragon. Sacred Stones' version of the main theme was also quite possibly better done than the main theme of any other FE title.
A Trusted Ruler. One of the most calming tracks ever written. First appeared in Path of Radiance, but beautiful enough to be re-used in Radiant Dawn. The latter game also remixed it into a boss battle theme very late in the game. Yes, a boss battle theme - Wisdom of Ages. And it WORKS.
It doesn't hurt that it plays for Dheginsea, That One Boss. Expect to hear it a lot in that chapter.
Heron galdrar. All of it. For an example, listen to the galdr of rebirth - it's less than half a minute long and it still manages to be one of the game's most beautiful themes.
The character promotion song Moving Up deserves a nod for being pure epic. This song is made even more badass when you actually see the scene of the character you have nurse from the beginning of the game being bless by the heavens to take their rightful place as your new destroyer. For reference look at Ike's promotion scene around 2:31 and see just how cool it is to become a lord. 
Father's Back is a particularly moving song, full of melancholy and sadness. It plays after Greil's death, leaving 2 orphans behind. Mist is devastated, and soon after begs Ike to not die too, him being the only family member she has left. All the elements are in place for a Tear Jerker moment.
Side Battle is a phenomenal remix of "Light and Dark" from Seisen no Keifu. Sadly, it only plays in trial maps.
Fire Emblem: Radiant Dawn has Pray for Victory, the song that plays on the Preparations Screen in all four Endgames. A powerful theme that gets the player pumped for the final battle(s).
Additionally, the Black Knight's theme in its prequel, Path of Radiance. The song was made even more awesome in Radiant Dawn with the subtly altered The Black Knight Lives. And what could be a more fitting and badass name for his battle music be than Unstoppable Destiny?
Radiant Dawn has some standout pieces of music that didn't make it into Brawl. The biggest one by far is the final boss music, A Grasping Truth, 9 minutes long and with an epic feel to it the entire time. It does have to be pretty epic to beat out Ascent, played on the chapters right before it and definitely an awesome track in its own right. Then there's Bearer of Hope, played during all of the defense missions in that game. And of course, Beauty Is A Mad Mistress, the remix of Power-Hungry Fool.
Don't Speak Her Name!. It plays throughout Chapter 10, immediately after Emmeryn's sacrifice and does an amazing job of setting the mood for the chapter. It became an instant fan favorite, and it's considered one of the best music themes in the entire franchise, which is saying a lot. BGM Override being in full effect only gives the mood a greater weight - the series is known for not using that trope, and the contrast of its usage here is phenomenal.
Conquest and its Ablaze version. The non-ablaze is already a calm and beautiful piece that welcomes you to explore the world of Awakening, and it's ablaze is undeniably one of the best battle themes to kick some Risen/Spotpass team ass to. What's more, while it's mostly an original tune, remixed notes of the original Fire Emblem theme come out in glorious spades towards the end of the songs. Even better; the best aspect about these songs is that they're so good that they fit perfectly on any map they're played on.
Storm Clouds and its Ablaze version; hoo boy, do these songs darken the atmosphere (and they are usually played when things get really tense story-wise). These songs remind you that you cannot afford to mess up here while intensifying the battle and absolutely making it more epic at the same time.
Duty and its Ablaze version. It's a relatively nice tune that is first introduced in Chapter 3: The Warrior Realm (fitting for the song's first appearance). They set the mood of some good ol' fashioned fighting and that the fightings going to get real serious, with a real gauntlet-esque feel to it.
Destiny and especially its Ablaze version. This theme appears in the mildly intense battles. Except that they make "mildly intense" sound "frigging epic", somehow!
Divine Decree and the Ablaze version, does a good job setting the mood for a climactic battle. Particularly in how the music in Chapter 23 switches from Chaos to Divine Decree, once Validar's plan is foiled.
Chaos and its Ablaze version is deliciously eerie and tends to play in latter chapters, where the Grimleal has the upper hand.
Id~Sorrow, the reflective and moving version of the Avatar's theme used for a late-game scene where Lucina cannot bring herself to kill the Avatar to prevent the ascension of Grima.
Mastermind, Gangrel's and Walhart's boss theme, is absolutely fantastic. The piece used as an intro for it is also really cool.
Id~Purpose, the Triumphant Reprise of the Avatar's theme, redone for the Final Map and Grima's Battle. In addition, it works the Fire Emblem Main Theme into its chanting. There's also the theme before that which is used to build up to it: Id~Return!
Also from the DLC, Id~Hope! Plays during the battles against the Future Past bosses who are all affiliated with the Avatar in some way (as the "Id" part gives away). AKA the Morgans and another version of Grima.