The following are songs in Super Smash Bros. Brawl and their origin.
Delfino Plaza - This is the original song from Super Mario Sunshine. As the name suggests, it played on the Delfino Plaza overworld. The second part to the song reflects that when you're on top of Yoshi.
Title/Ending - This happy song played in the end of Super Mario World when you met all of the game's enemies.
Main Theme (New Super Mario Bros.) - This played in the overworld of New Super Mario Bros. and was originally composed by series vet Koji Kondo. This remake, however, was under the supervision of another classic - Shogo Saki of HAL.
Ricco Harbor - Like Delfino Plaza, this is the original and not a remake. Also like Delfino Plaza, the latter half reflects the song that occurred when you rode Yoshi.
Ground Theme (Super Mario Bros.) - Quite possibly the best known song in all of video gaming, the original was composed by Koji Kondo - and this remake is too! The classic latin feel to it is intact and better than ever. It played on the overworld of Super Mario Bros. and has been remade a multitude of times.
Ground Theme 2 (Super Mario Bros.) - The same song as above, though not composed by Koji Kondo.
Gritzy Desert - This song occurred in the Shroob infested desert of Mario & Luigi: Partners in Time. In the inner portions of the desert you'd face the evil Petey Piranha.
Underground Theme (Super Mario Bros.) - Another classic that has been remade in nearly every Mario platformer. It originated in Super Mario Bros. and would play in the underground sections.
Underwater Theme (Super Mario Bros.) - This classic tune played when Mario or Luigi went swimming in the vast seas of Super Mario Bros. There's three different portions to this song - so be sure to listen to them all.
Underground Theme (Super Mario Land) - This one occurred in the, as the name implies, underground sections of Super Mario Land - the launch title for the Game Boy. It was one of the most notable songs of the title.
Luigi's Mansion Theme - This song played throughout the entire game of Luigi's Mansion in a variety of ways. It's a classic song and one of the most notable of the GC generation.
Castle/Boss Fortress - This is a mixture of two games - the castle theme from Super Mario World and the fortress theme from Super Mario Bros. 3.
Airship Theme - The airship portions of Super Mario Bros. 3 are quite possibly some of the most notable parts of the entire Super Mario Bros. series - they were challenging and fun and of course featured the ever popular Koopa Kids.
Mario Circuit - This song played on the four Mario Circuit courses of Super Mario Kart for the SNES.
Luigi Circuit - Played on the Luigi Circuit stage of Mario Kart 64.
Waluigi Pinball - Aww, one of the best songs of Mario Kart DS wonderfully recreated. Seriously, it has a catchy tune, though I'm sure a majority of you won't appreciate it! As its name implies, it originates from the Waluigi Pinball stage of Mario Kart DS.
Rainbow Road - This song was ripped from the game, and not thus is not a remake. It played on the final course of Mario Kart: Double Dash!!, and is one of the better songs in the Mario Kart series in my opinion.
Main Theme (The Legend of Zelda) - Possibly on par with the SMB main theme on the most notable songs of video games, the main theme of The Legend of Zelda has captured the hearts of many a gamers and has been recomposed tons of times. This is one of the best, as it's fully orchestrated, just as we like it! It played on the overworld of the original Legend of Zelda, though back then it was just bleeps and bloops. Now it features a wide range of instruments to satisfy the wants of Zelda fans. Of course, we've had orchestrated versions of this song before, even in the previous Smash installment, though this is, as aforementioned, one of, if not the best remake yet! Crank up the sound to 11 on this one!
Ocarina of Time Medley - This merges some of the ocarina songs from The Legend of Zelda: Ocarina of Time into one fantastic medley. A flute plays throughout and practically acts as the ocarina.
Title (The Legend of Zelda) - Basically a remake of the main theme of The Legend of Zelda and the dungeon theme, the latter of which has been considered by many as the greatest song in the entire series.
The Dark World - Players could hear this song in The Legend of Zelda: A Link to the Past when Link transported into the dark world of Hyrule and once he turned into a bunny. It's arguably the best song in the game.
Hidden Mountain & Forest -
Hyrule Field Theme - Another song from Ocarina, though as previously this is remade. It played once players entered the overworld, and acted as, sort of, the main theme of the game (well, maybe).
Main Theme (Twilight Princess) - This song played in the overworld of Hyrule in The Legend of Zelda: Twilight Princess, so it's sort of the Hyrule Field Theme of this game. It's one of the six (I think six!) fully orchestrated songs in the game, and certainly the most notable. It's no wonder they didn't remake it for this game - it's nearly perfect already!
The Hidden Village - This place played in that one abandoned village of Twilight Princess - you know, the one where you had to catch all of those cats! Yes, I know it played a bigger part, but that part was quite annoying in my opinion! Anyway, you can tell that it was composed by the same person who did the Twilight Princess main theme, as it sounds somewhat similar.
Midna's Lament - I recognized the song when I heard it, but don't quite remember when it played. There are a multitude of times where it could've played, but I'll have to check back later (no internet at the time! Writing on word!).
Great Temple/Temple - Yay! One of my favorite Zelda songs which occurred in one of my least favorite Zelda games - Zelda II: The Adventure of Link. A similar song was featured in Melee's Hyrule stage as well.