Well ever created is going a bit far but, there have been some great music from alot of games.  I think the majority would agree with me.

FF7 music simply because well its FF7, who isn't a fan?  Mostly the generic fight music,

Shadow of the Colossus.  This game was considered a master piece in both game play and music during its time.

Megaman 2's Dr. Wily stahe 2! This song is the epitome of epic when played on an electric guitar.

http://www.youtube.com/watch?v=9MvCwJiflBw&feature=related

I personally liked the ending song for castlevania:symphony of the night

Song was called "I am the wind" cant remember the singer though.

http://www.youtube.com/watch?v=nU0C1xHS8BI

AoC had the best music I have ever heard in a MMO and it fitted perfectly, here is the best track imo:

http://www.youtube.com/watch?v=deDNzOYHu-4&feature=related

Guild wars, composed by legendary MMO / Game music composer, Jeremy soule.

Braid.

http://www.youtube.com/watch?v=vTy6E17-yMU&feature=related

I assume we're talking about games in general, not MMOs. If it's MMOs only my favorite music would have to be from Lineage II then.

Hands down I think the "Teldrassil" zone track in World of Warcraft. Now don't flame me for that, it's simply a beautiful song in a game full of ugliness...

"False Images" Track from the WInter Missions Carnival on Phantasy Star Universe Ambitions of the Illuminous by Far.

http://www.youtube.com/watch?v=8N5ODEGR1KQ

First Dungeon Keeper Intro

Elder Scrolls 3: Morrowind theme

Elder Scrolls 4: Oblivion theme

Both different versions of the same piece composed by Jeremy Soule.

The theme from Mass Effect is also very good.

There's a lot of good and memorable VG soundtracks out there, Metal Gear Series, FF Series, etc.

By far my favorite soundtrack is EvE's. Nice and minimalist, and very atmospheric.

The music used for DAoC's night time cycle is one that sticks out to me as well.

Originally posted by Scot

AoC had the best music I have ever heard in a MMO and it fitted perfectly, here is the best track imo:

http://www.youtube.com/watch?v=deDNzOYHu-4&feature=related

Agree, AoC has imo the best music in the MMO category, even if I prefer the Tortage tracks.

Outside this genre, I prefer this one :)

http://www.youtube.com/watch?v=fduqstJHgFY

The opening in Xenosaga 2

The Fatal Fight song from Xenosaga 2

The "Character Battle" and "ES Battle" themes from Xenosaga 2

The Song from Battling with Tiamat in Xenosaga Episode 1

The Gale and Brink of Death songs from Chrono Cross.....and almost any Chrono Cross song

The Battle Theme from Legends of Dragoon

These songs from Kindgom Hearts and Kingdom Hearts 2:

Kairi

Kairi 1

Kairi 2

Kairi 3

Namine

Roxas

Forze De Male

Scherzo Di Notte

Sanctuary

Dearly Beloved

Scythe of Petals

Destati

Fantasia all marcia

Passion - The Tokyo Philharmonic Version - Instumental

And the trailer in Galerians: Ash, with "O Fortuna"

Also any Final Fantasy Game Song remade by The Black Mages

I really enjoyed the music in Dark age of Camelot one of the few games I would leave the sound on for.

http://www.youtube.com/watch?v=_iASSYsH8Oc < call to arms

Lineage 2 had some amazing music. My faves are:

Dion Town Music:
http://www.youtube.com/watch?v=62Nl7CmdwUU

 Login Main Theme (C1)
http://www.youtube.com/watch?v=2gZEH0Z9--g
 

Purely due to its nostalgic value, I'd have to go with the music from EQ1.  A couple songs that I still occasionally hum without really intending to are the boat themesong, the Qeynos music, and (my personal favorite) the Rivervale song.

Haha, now I'll have to go look up the .midi files again and have a listen.  Thanks a lot, OP

I actually really like the LOTRO soundtrack, although each track is pounded into my head from hundreds of hours of play :/

Otherwise, the only two games tunes I that I think are catchy:

That themesong from the Battlefield games, that is the best song I have ever heard.

Battlefield Heroes' new themesong is pretty catchy too. Still, the original BF theme wins,

1942 Theme: http://www.youtube.com/watch?v=Gylo7Ak6z3Y

2 Theme: http://www.youtube.com/watch?v=pE6MJweDscQ

2142 Theme (my favorite from the 4. It's much more rousing, kind of preparing the player for battle): http://www.youtube.com/watch?v=3rbSfCfa2-M

Heroes Theme: http://www.youtube.com/watch?v=Lz0v-qixpOI

The Battlefield Theme performed by a symphony: http://www.youtube.com/watch?v=BdXEtTWEVtk

The Mass Effect music is defnitely good too, very... 'epic' soundtrack, along with that of the LOTR movies.

Games have songs?

Seriously, soon as I install one first setting I change after video  is the sound and turn off all in game music.

Forgot games actually had musical scores.

Medieval II: Total War battle music is great. I think some of the WoW music is well done, even though there's not much of it (they did a great job with Northrend. Grizzly Hills music is uplifting and fits with the outdoorsy, untamed wild theme of the zone). As linked above, some of the Battlefield theme songs are nice. I only liked one song in AoC really, which was the one from Conall's Valley.

Can't really think of many others. Most games have music that just blend into the background and don't really stand out.

Originally posted by Comnitus

Medieval II: Total War battle music is great. I think some of the WoW music is well done, even though there's not much of it (they did a great job with Northrend. Grizzly Hills music is uplifting and fits with the outdoorsy, untamed wild theme of the zone). As linked above, some of the Battlefield theme songs are nice. I only liked one song in AoC really, which was the one from Conall's Valley.

Can't really think of many others. Most games have music that just blend into the background and don't really stand out.

I think those are the best musical pieces, they help set the mood and you barely notice they are doing their job.

They symphonic version of battlefield 1942 was slick.