Possible spoilers in the videos.
Phantasy Star Online - Can Still See the Light - Epic piece, slow and calm, but at the same time very poweful.
Valkyria Chronicles - Succeeded Wish - Poetic, gives me watery eyes.
Z.O.E. II - Beyond the Bounds - As fast and upbeat as the game itself, fits it perfectly.
Soul Blade - The Edge of Soul - Sets the mood of the game in an excellent way, still one of the best intros ever.
Metal Gear Solid - Snake Eater - Awesome, gives you '70/'80 Bond vibes.
Super Smash Bros. Brawl - Main Theme - That latin chorus, very nice.
NiGHTS Journey of Dreams - Dreams Dreams (Will Version) - Dreamlike and refreshing.
Donkey Kong 64 - DK Rap - Funny and crazy intro.
Skullmonkeys - Little Bonus Room - Creepy as fuck.
Portal - Still Alive - One of those catchy songs you can't ever get out of your head.
Portal 2 - Want You Gone - Great follow-up to the amazing piece from the first game.
Portal 2 - Cara Mia Addio - Lyrical masterpiece, such feels.
Fragile Dreams - Hikari
Fragile Dreams - Tsuki no Nukumori - Both are very sad but absolutely beautiful songs.
Time Hollow - Theme Song - Nice ending to a nice game.
Kingdom Hearts - Simple and Clean - When coupled with the CG cutscene it's the best ending song ever, I love the way it started out of the blue.
Kingdom Hearts II - Sanctuary - Great intro, Utada's work in general is amazing by the way.
FFX - Suteki da ne
FFVIII - Eyes on Me - Great love songs.
FFX - Otherworld - Metal in my FF? Sure!
FFX-2 - Real Emotion - It got a lot of flak in the past, but I appreciate it for what it is, a nice j-pop song.
FFVIII - Fithos Lusec Wecos Vinosec - Dreadful in a good way.
FFXV - Somnus - Best thing to come out of FFXV so far, one of my favourite pieces ever in the series.
BONUS:
Twitch Plays Pokémon The Song by Tai Reflections & Vulkain - Perfect fit for the original chaotic stream.
EDIT: Also I forgot TWEWY, everything about TWEWY's OST is good, though I dunno about listening to the songs outside of the game.
EDIT 2:
FFVI - Opera Maria and Draco - They re-created a 4 tracks opera inside a game, how could one not be stunned by its beauty?