Dragon Quest/Awesome Music

The Overture March (also known as the Dragon Quest Medley or just Overture). (Symphonic). Behold, a song instantly recognizable instantly to the entire country of Japan for the past 25 years, it has been remixed literally thousands of times and prefaces every Dragon Quest game.
King Dragon, the final boss theme. (DQ9 Symphonic version)
The overworld theme of the first game, has been included in many games, not just the remakes of the original DQ1.

"A Lonely Youth", the overworld theme that plays when you start the game with the Hero going solo for the first part of the game.
GBC Version
"The True Evil", The final battle theme with Malroth.
- It's even more awesome in Dragon Quest IX!

The Overture remix, that only plays after we see the Hero prepare and proceed on his journey or rather, that we see that he has failed on his journey, or more specifically (in the GBC remake) when the king declares that you are the inheritor of his legacy and the world's last hope.
The Overworld theme, appropriately named "Adventure", gives players a foreshadowing of epic the journey is going to be.
- SNES Version
- Orchestrated Version
Heavenly Flight (Symphonic). You can take your airships, I'll take riding on the back of a giant sentient bird deity any day.
Battle Theme
Boogie-Woogie, the lobby theme for the Monster Arena and the Pachisi Board minigames. Sadly, it was not in the original NES game.
- GBC version
- Itadaki Street version
Hero's Challenge -- the first time a Dragon Quest final boss has had two themes -- plays when you finally use the Sphere of Light to weaken Zoma so he can be defeated for the first time in history. (Symphonic from DQ 9)

The final Overworld Theme that plays when the entire playable cast has finally joined together, Wagon Wheel's March, is quite heroic and sets the tone of that point in the game well.
- Its Itadaki Street DS arrangement is even more epic.
Casino Rag, the gambling area for the game.
- Fortune/Itadaki Street DS arrangement
In the original version, the credits theme was pretty good, but in the remake they turn it into an all out Fanfare.
Evil One, which you got to hear twice in the game (Against Estark and agains the final boss's first 6 forms). It would later go on to become Estark's Leitmotif.
- The DS remake's version is also awesome.

The Overture makes its appearance here, but another special note of just when it appears is required: It's only after we watch the hero's mother die in childbirth, the crushing silence broken by his newborn cries that the overture begins. This is how you add atmosphere to a game.
As is usual for the series, the Overworld theme, in this case called Toward the Horizon, is excellent.
"Racing Slimes!"
Violent Enemies, the normal battle theme, is one of the best in the series (also its DS version.) In addition, the Boss Theme isn't too shabby either. To top if off, there's the Symphonic version of both these themes.

Through the Fields - Overworld theme.
- Another World - its Mirror World counterpart, is slower, more solemn, perfect for a dream world.
Courageous Fight - the standard battle theme
Brave Fight - used only once when facing against Mudo/Murdaw.

An Orchestrated Remix of the Overture, where the Dragon Quest dev team and Level 5 show off their fancy new engine to the tune of an Orchestrated remix of the song all while a pair of birds fly for miles using the in game engine and no load times. Epic. Just Epic.
Rhapthorne's theme, Great Battle in the Vast Sky. More subdued than the typical last battle, but only because Rhapthorne may possibly have pulled off the biggest Kick the Dog moment in Dragon Quest History. It also contains Ramia's Theme from Dragon Quest III mixed in -- For good reason, as you are riding on her back as you fight him.

Everything. Just everything. Featuring remixes of nearly the entire Dragon Quest OST library, all done in glorious symphonic remixes. They went all out for the series' glorious return to the west, and it shows.
Observe the Dragon Quest 9 Overture Remix, now with a buildup and an orchestra playing it (the first time they have skipped the chiptunes and went straight for the big band).
Some examples of the remixes: Zoma (DQ3), Rhapthorne (DQ8), Dragon Lord (DQ1), Estark (DQ4).
And the final battle theme, which has the Overture mixed in with it.