For some reason, while you're playing a game you would listen to music at the same time. At certain points in the game you would listen to a particular song, maybe to add "effects" to the game, or specifically to remind you of that scene in the game.
In my case, I would listen to the opening and ending theme songs of Gundam SEED Destiny while playing Radiata Stories. One particular song that caught my attention was Vestige by Takanori Nishikawa (T.M. Revolution), the opening theme in Final Plus. Because of its sad melody, I listened to Vestige while I was at the near end of the human path in RS, where Ridley gets killed by the silver dragon and dies in Jack's arms. And yes, it made me shed tears, maybe because of the sadness expressed in the song and seeing Jack lose someone important.
As for the fairy path ending, I listened to See-Saw's Kimi Wa Boku ni Niteiru or "You Are Similar to Me". This is the 4th ending theme of GSD.
(N.B.: You can check the music videos at YouTube in case you haven't heard them. And for some reason, I like mixing RS with the songs of GS/GSD, maybe because Shinn Asuka and Jack Russell are both barking dogs in their respective series.)
I usually listen to the soundtrack of the game while playing it the first time. I generally refrain from listening to anything from the game's soundtrack before I actually get around to playing it, so I can have the new game experience freshly unspoiled for myself.
I'll sometimes listen to random metal tunes if it's a replay. But only if I've listened to the game soundtrack so much that I know it like the back of my hand.
I have a really odd one, but it's just tradition for me to listen to the album You Can't Stop the Bum Rush by Len while playing Ape Escape, especially the first one. That reminds me, I really want to get the third. xD
Also, Led Zeppelin (specifically the first disc of that four disc compilation set) when playing Ace Combat 4/5. Something about "Whole Lotta Love" really gets me in the mood for aerial combat.
And Black Sabbath for Half Life 2, specifically HL2 Deathmatch.