The songCease to Exist aka Pokey Means Business used in the battle against Giygas in the "Devil's Machine". It starts out like a throwback to traditional 8-bit RPG battle music, then unexpectedly erupts into something... unsettling, yet even more awesome.
A simple but effective Trash Metal remix that'll get your blood pumping. Unlike a lot of other remixes, this one keeps the tempo in both the fast and slow parts accurate.
And then a remix that throws away all restraint, culminating in the musical insanity the battle strove for.
The Giygas Battle Music that plays during his second form. Insanely creepy and way ahead of its time, this Harsh Noise backdrop sounds like something from Silent Hill, or the love child of Merzbow, Autechre and Aphex Twin. Certainly not the kind of music you expect from a final boss fight in a JRPG. Those death cries over the static set in musical tone were one of the most jaw-dropping death scenes of the generation.
For some 1950's rock 'n' roll goodness, you have a choice for the 'New Age Retro Hippie' battle theme from the first and second games, and 'Rock and Roll' (either 'Mild' or 'Spicy') from Mother 3.
Bound Together; "48 songs Nearly 3 hours of music 8 bonus songs including demos and alternate takes the VG Frequency radio show from October 29th which featured the debut of Bound Together." Download it and give it a listen, If you have any love for Earthbound, it will take you back.
Porky's Porkies is a bizarre, yet supremely awesome, 8-bit track from the third installment.
While not complete, this guy's remix probably counts as well.
By the same token, that little song that plays when DCMC comes to the rescue. Surprisingly good, considering it's something most people probably won't hear all the way through.
One Word: Mother!? As if Chapter 6 of Mother 3 wasn't poignant enough, this song really drives it into absolute Tear Jerker territory.
Dry Guys and its faster remix Even Drier Guys. Its whimsical and slightly melancholy tone coupled with an accordion and an excellent piano solo captures the top quality standard for music in the game as well as the tone of the story.
Run, My Dog, Run! from Mother 3. It's basically the soundtrack to Boney's Moment Of Awesome. Whether or not Boney is the most powerful character, that scene singlehandedly solidified his "Boney is awesome" status forever.
Speaking of Theme of Love, there is also the vocal version of the song which is sweet and heartrending no matter what language it's being sung in.
Fan remixes of Theme of Love are no slouches either. There's this localized version of it in English, with lyrics translated by the person behind the fan translation of Mother 3, Tomato, so you can be sure this English version of the song is really as accurate as it can be in the language without sounding too awkward.
Piggy Guys is so awesome that it received an epic remix that contains another song which SHOULD have been in Brawl.
Though they were basically a spinoff of the Runaway Five from Earthbound, DCMC was an in-game rock/jazz band that took a few of the best Awesome Music candidates from the game and made them a million times more Awesome. For example, the "DCMC Theme," a remix of Duster's "Mind of a Thief" tune.
Fate and Serious from Mother 3. The way to combo these songs is pretty clever, too.
Natural Killer Cyborg. An amazing rockin' theme that assures the player they are going up against a massive super-robot, and it's even got a bit of 'Beat It' mixed in for extra awesomeness.
At the end of Mother 3, the most beautiful songs from the trilogy are reprised, including (surprisingly) the MOTHER 1 main theme. What makes it go into absolute Tear Jerker territory, though, is the reprise of Pollyanna, played as you take the boat ride to Porky's room. What makes it so sad is that Porky has crossed the Moral Event Horizon so many, MANY times, in such horrible ways, that you know there's no way he can have a happy ending, and also that you're surrounded by mementos from Earthbound: turns out he really did like Ness as a friend after all, huh?
Bon Voyage Amigo. Only a game like Mother 3 can make what's supposed to be the joyous occasion of completing your party, a Tear Jerker moment.
It Is Finished/It's Over, a remix of the Love Theme played at the climax of Mother 3 where The Masked Man AKA Claus finally comes to his senses and says one last goodbye and apologizes to Lucas before killing himself. It's... very sad.
Gentle Rain, a very peaceful and soothing track. The Mother 3i remixed version combines this with a remix of Confusion, the music that plays when Flint finds out Hinawa has been killed in a not precisely tactful manner, perfectly conveying a sense of shock and loss.
The entire game kicks off with a little song called Fun Naming. It's a gentle, moving piece that helps welcome the player to the Mother 3 world.
And after that, this song accompanies a sweeping view over the Nowhere Islands.
The Attic's A Dungeon!? is pretty easily overlooked, playing in only one pretty short area, but that doesn't stop it from being an awesome beat.
Monkey's Delivery Service, though not as sad as the aforementioned music, is still damn hard to listen to without getting teary, as it embodies all the shit Fassad put Salsa through.
After going through a long adventure, seeing the ending, the "The End?" screen and its secret, you're treated to a roll call of the characters you met in the game, set to this awesome medley, appropriately called Curtain Call. The way it starts, you can almost hear an entire audience roaring with applause in your head.
LOG-O-TYPE, a grand, majestic theme that plays when the Mother 3 logo appears in the intro of the game. To quote a Youtube commenter, "The first time you heard this, you knew you were in for one hell of a game".
"Accelerono". It's used as the battle theme for the walking tombstone enemies, whose gimmick is that they walk towards you... slowly... until they very painfully strike. And the music sounds slow and lumbering at first, until it gets faster... and faster... and faster...
The song for the credits, 16 Melodies, combines all three main themes from each Mother game. It starts out with brief snippets of "Theme of Love", "Eight Melodies", and "Smiles and Tears", then plays the first full verses of "Eight Melodies" from Mother 1 and Earthbound'''s "Smiles and Tears", and finishes with the full version of "Theme of Love" which ends its last remaining verse very triumphantly. It's uplifting, tearjerking, and heartwarming all at once as it embodies the strong end to this trilogy of great games.
The Game Over theme, Stand Up Strong, is - like pretty much everything else in Mother 3 - beautifully tearjerking, in that it embodies the serenity of death: it's pretty much a funeral tune, played with an organ. It is, essentially, "you can now rest in peace" in musical form.
Special mention should go to Azure Studio's project. Though it may be a Fan Sequel, it looks as every bit as awesome as the official titles, and it's no slouch in the music department either. A small example is this remix combining both MOTHER 1's "Battle Against a Dangerous Foe" and Earthbound's "Sanctuary Guardian" themes.