I'm surprised there hasn't been a thread about video game music, but I suppose I'll be the one to create it.
Video games are fun, because they're interactive. But looking back, it's the music I remember most. It's the music that makes the games so nostalgic, and what makes me miss playing them the most.
Through my childhood up to early adulthood, I've played who knows how many video games. I'll give you the top five video games with my favorite music. (Make sure the volume on your computer isn't turned up awfully high if you choose to click the links and hear the music.)
5. Super Mario Bros.
I'll start with the classic. These songs are 100% purely nostalgic, but they're also pretty catchy, too. Admit it, the Main SNES music puts a smile on your face every time you hear it. 
4. Star Wars: Knights of the Old Republic (Jeremy Soule)
Upon inserting the rented KOTOR disc into the tray for the first time and hearing the theme of the Old Republic on the main screen, I wasn't aware that I was about to play the greatest Star Wars video game ever made. Jeremy Soule made the experience that much better. Even running around the apartment complex and browsing through the typical city life never felt like a waste of time, simply because of the music. Just imagine if your life sounded like this while walking around in public.
3. Spyro the Dragon (Stewart Copeland)
My top three aren't just single games, or a select few standout soundtracks anymore. These are whole franchises that have made a living creeping their way into my iPod with their music. Mainly known for his career with the band "The Police", Stewart Copeland has also found a home with my own generation of Spyro fans. "Jaques" is without a doubt the most recognizable song from the entire franchise, but it's also hearing bits like Evening Lake that make me yearn to go back to places like...well, Evening Lake. 
2. Command & Conquer (Frank Klepacki)
"We are going to have to act, if we want to live in a different world."
And with that line, followed one of the most entertaining experiences I've ever had playing video games. Back when I was still in elementary school, I used to beg my older brothers to play this game. I longed for the power to control an unlimited number of tanks, so I could overwhelm those damned Obelisk of Light defenses.
1. Halo (Marty O'Donnell and Michael Salvatori)
The Gregorian chants. The orchestral beauty. The sense of scale every time you delved deeper into the intense science fiction world of the Halo rings. And to top it all off: the fact that the more down-to-Earth (literally and figuratively) ODST had absolutely none of that - and still had the best soundtrack out of any Halo game. This post is already long enough, so I'll just list a select few of my favorite tracks.
[url=http://www.youtube.com/watch?v=H20Ok5BKR-Q&feature=relmfu]"Perilous Journey" - Halo: Combat Evolved
"Peril" - Halo 2
"Delta Halo Suite" - Halo 2
"Behold a Pale Horse" - Halo 3
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Honorable Mentions: These are examples of music from games that left an impact - albeit not quite as much those as my top five - but still enough that certain songs bring back good memories.
Tetris - Not much, but it's still iconic as ever.
Blinx: The Time Sweeper - There's just something about this beat that brings out your inner childhood.
MechAssault - ALL YOUR BASE ARE BELONG TO US
Sonic Unleashed - Confession: I've never even played this game. But I discovered the music anyway, and I'm still having regrets about not playing it.
Kameo: Elements of Power - This music is worthy of any fantasy epic.
I hope others are willing to share their own flavors as well 
Kind of want to be as explanatory as you, but seems I can't fight lazy, so I'll be brief
Legend of Zelda
Enjoyed the soundtrack from all the Zelda games, though most notably The Wind Waker. That one's music I found quite fun and soothing.
Castlevania
I'm going to say I like the music from all the Castlevania games, but, in truth, I'm mostly thinking about Bloody Tears. Never get tired of that song.
Atelier series
Another series I enjoy the soundtrack from all the games. Atelier Annie and Mana Khemia in particular.
Persona 3
I'm going to include Persona 4 as well, but overall I prefer 3.
World of Warcraft
Though I'm becoming ever more critical of World of Warcraft, the one thing which continues to impress me is the music.
I'm sure they're several other games I'm forgetting about, but if they're really good enough I guess someone else will mention them
Hehe that's alright, I just want to encourage others to share some of their favorites. Couldn't help myself though; I'm generally a shy person but I can also get carried away sometimes when I try to be sociable ^_^;
Solatorobo, Radiant Historia, Flower, The Metal Gear series all had amazing OSTs.
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I'll start with the classic. These songs are 100% purely nostalgic, but they're also pretty catchy, too. Admit it, the Main SNES music puts a smile on your face every time you hear it.
I actually had to learn that on bass for a recital a few years back - fun song to play.
For me, I'd have to say the Fable music on the first game - a very good use of minor triads in chord progressions played on the harp, just gets me everytime I hear it.
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So many to choose from, and so many excellent and classic nominations already. However, I'm a little less mainstream, on the top of my list is the soundtracks from one series in particular: Lunar Silver Star Story Complete & Lunar Eternal Blue Complete. Other more notable soundtracks: Xenogears, Final Fantasy 6 and 7 (because someone had to), and both Chrono Trigger and Chrono Cross.
Xenogears definitely has an awesome soundtrack and it also had the same composer who worked on Chrono Trigger, right? Chrono Trigger also had a great soundtrack.
I'd like to mention Shadow of the Colossus. Though some of the songs are actually used at least twice, each one seemed to fit in with the respective battle, making them all the more engaging for the players.
Another game I really liked the soundtrack to was Final Fantasy XI, a lot of the areas had some very pleasant music to listen to at times and I'd simply travel to those areas to listen to a specific background track even when I knew there were higher level enemies in the area.
And lastly I would like to mention Phantasy Star Online, Sonic Team did a great job making the songs for this game. Again, I sometimes find myself clearing entire areas and just staying behind for a bit to listen, luckily there was also a sound test option for this one. Though it did have some tracks from other games you couldn't simply play from there.
There are definitely more games, but these are some of the more frequently listened to OSTs for me on the Youtube.
Glad to see that this forum was recently made.
Here some of my favorite VG OST's:
1. God Hand
2. The No More Heroes Series (the original being my favorite of the two)
3. the Street Fighter EX Series (SFEX2+ being my favorite)
4. Streets of Rage 1 and 2
5. The Megaman X, Zero, and ZX series.
6. Shadows of the Damned
7. Bayonetta
8. Viewtiful Joe 1 and 2
9. Demon's Crest
10. Gundam Wing Endless Duel
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Awesome; I'm compelled to just sit down and listen to some of these suggestions!
Bionic Commando Rearmed has an awesome remixed soundtrack and so does the Mushihimesama series.
Then there's the whole Ghost n' Goblins/ Ghouls n' Ghosts series.
The Capcom vs. SNK series and especially the arranged versions of all three different versions of Street Fighter 3. Almost every Street Fighter game has had good music in my opinion, especially Alpha 3 and SF2.
Etrian Odyssey has some great music as well. The arrange albums are definitely where the soundtracks reach their potential.
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