The Overture March (also known as the Dragon Quest Medley or just Overture). (Symphonic.) Behold, a song 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.
The ending theme, a triumphant conclusion which just says, "You did it. You saved the world from evil. Congratulations!"
The ending theme, My Road, My Journey, really sells the idea that your journey to save the world has come to a triumphant end, with one Reddit thread even stating that it sounds "too much like music that would play when the bride walks down the aisle". The orchestral version of this theme is used to great effect in the climax of Dragon Quest: Your Story when Luca vanquishes the virus with the vaccine created by Gootrude, Luca's Slime companion who reveals himself to be an antivirus program.
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 just how epic the journey is going to be.
Heavenly Flight (Symphonic). Riding on the back of a giant sentient bird deity beats riding in an airship any day.
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 heroic and sets the tone of that point in the game well. Its Fortune Street DS arrangement is even more epic.
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 against the final boss's first 6 forms), 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 apparently 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. Its DS remake is equally excellent.
Given that love is a big aspect of the game, naturally it needed a powerful theme to match the emotion of the moment. The orchestral version especially helps it soar like a bird.
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).
(also known as the Dragon Quest Medley or just Overture). (Symphonic