Wildfire Riders

I gotta admit, all this is close to my heart. I'm a nerd forever.

So, Fells posted Radical Dreamers, the ending theme to Chrono Cross. Here's an very relaxing instrumental cover. Chrono Cross itself has an astonishingly good score, and I recommend kicking back and enjoying the following:
Scars of Time (opening theme)
Chronopolis
Fort Dragonia

Ceil also mentioned music from Touhou Project. I can state sincerely that nearly every piece of music composed for it is good (the creator, who goes by the pen name ZUN, is best described as a sythesizer virtuoso), but you--yes, you--must hear the following:
Evening Sky
Autumnal Waterfall
Bloom Nobly, Ink-Black Cherry Blossoms

And now for a few miscellaneous pieces of old-school greatness, in no particular order:

Final Fantasy VI - Cyan's Theme
Final Fantasy VI - Shadow's Theme (A ninja with spaghetti-western theme music? Brilliant.)
Illusion of Gaia - The Great Pyramid
Chrono Trigger - The Singing Mountain (A track that never actually made it into the original game, but happily did make it's way onto the DS port)
Donkey Kong Country - Aquatic Ambiance
Zelda II: The Adventures of Link - Palace Theme (If you haven't heard this before specifically, now you know where the music from the Hyrule Temple stage of Super Smash Bros. Melee came from!)
The Legend of Zelda: A Link to the Past - The Dark World (a particularly good orchestral cover)
Xenogears - Awakening
Brave Fencer Musashi - Far Into the Sky (main theme)
Final Fantasy VII - Anxious Heart
Mega Man 2 - Dr. Wily's Castle - Stage 2 (Sing with me now: "Urutora-man! Urutora-man SE-BEN!")
Mega Man X - Intro Stage
Diablo - Tristram
Secret of Mana - Fear of the Heavens (opening/title theme)
Secret of Mana - The Oracle (Some trivia: That rapid-fire "percussion" that pervades the song is based on a form of Indonesian ceremonial chanting known as kecak. It involves a large group of perfomers chanting in sync, and the effect here is decidedly eerie, particularly considering what you fight while this plays. The down-side is because it has such an elaborate sound, there doesn't seem to have been any attempts made to work it into remixes or covers of the tune--despite how faithfully the composer replicated it on that old SNES sound chip!)

Any of those bring back memories?

And since I can't resist, some from newer generations:

Silent Hill 2 - Theme of Laura
Xenosaga Episode I - The Miracle (Latin choirs are not uncommon, it's true. But this is probably the single most epic use of it I've heard--and it's done by the same guy responsible for Xenogears and the Chrono games.)
Xenosaga Episode III - Godsibb
God of War II - Main Theme
Shadow of the Colossus - The Farthest Land

LATINCHOIR LATINCHOIR SEPHIR-LOCHE!

I don't have links, because searching on dial up makes me QQ. But the Dynasty Warrior games all have pretty decent music, if not a bit weak-thrashy.

The Diablo Tristram stuff gives me chills down my spine. I spent an entire day and night trying to finish Diablo 2 when I was in year 9 or 10. This is all freaking me out a little. XD

All these are by Powerglove. Awesome video game cover band.

FF6 Decisive Battle

FF7 Boss Battle

Castlevania

Mortal Kombat/Mega Man 2: Metal Man

Mega Man X: Storm Eagle (Favorite)

Power Rangers (original)

Powerglove is so awesome.

than wrote:
Mega Man X: Storm Eagle (Favorite)

You know, for the longest time, this was always the first specific piece that popped into my head when I thought "rock music in a video game". Hearing it being shredded out is just gratifying. Ladies and gentlemen, we reap the benefits of being part of the generation that grew up with this, who now apply well-honed talent in tribute to it. Metal talent, in this case.

Browsing Power Glove's stuff, I found this medley of Zelda songs appropriately entitled Power, Wisdom, Courage and a deliciously symphonic mix of themes from Final Fantasy IV.

On the subject of Zelda medleys: If you've not heard this blend of songs that were played on the titular instrument in Ocarina of Time from Smash Bros. Brawl, holy shit, click that link!

Oh, and edit: On another semi-obscure old-school note, everyone remember to beware the forest's mushrooms in Super Mario RPG. Or remixed for Brawl, if you prefer.

Super Mario RPG was an underrated gem of a game.

I wouldn't say "underrated" so much as "unjustly unknown". The same applies to the Paper Mario and Mario & Luigi RPG series, which have, in the words of a reviewer, been quietly excellent for years.

Also, hey! Have a listen to Korobeiniki, the operatic piece on which the immortal "Tetris Theme" was based.

70's Japanese techno (kinda like Japanese Kraftwerk) that inspired a LOT of videogame music. Music and videoclip was very advanced for its time.

Yellow Magic Orchestra - 'Rydeen'
http://www.youtube.com/watch?v=sk6o4GWFIV8

I will constantly host an undying love of the Gourmet Race song from Kirby, especially with the AMAZING VERSION from Brawl. (and bonus Snoop Dog)

If you haven't heard Hyadain's work, I highly recommend it. He takes basic songs (like the Super Mario Bros' theme) and reworks them with hilarious or endearing lyrics and excellent vocals.

Lans is utterly right about ZUN - some further amazing ones:

Septette for the Dead Princess
The U.N. Owen Was Her?
Reach for the Moon, Immortal Smoke

As always, the (completely fucking mad) Touhou fan community must NEVER be left out when discussing these games. The music they do (the videos I linked earlier are a remix/cover of this, from one of the much older games) is mindblowing:

Orchestral Arrange of Septette for the Dead Princess
One of the most popular to remix: The U.N. Owen Was Her? (Virus Key, Bloody Scarlet and Metal)
Remix of Reach For the Moon, Immortal Smoke (Eternal Nocturne)