My favorite intro music is probably Opening Demo from A Link to the Past. (unpopularly) I'm not too big of a fan of LTTP music but I love this one song a ton. (shortened link so it doesn't show as a video in the post.)
I also like SM64's opening song, Undertale's, and Shovel Knight's main theme.
"For I am a sinner in the hands of an angry God. Bloody Mary, full of vodka, blessed are you among cocktails. Pray for me now and at the hour of my death, which I hope is soon. Amen." - Sterling Archer, aka "Duchess", aka "world's most dangerous spy".
The Meaning of Life, the Universe, and Everything.
I hope no one's too annoyed by anime style video game openings. I loved these when I had the first two redone Star Ocean series for the PSP (before they got stolen from my house)... Can't find the music videos for them though... I'd also throw in Star Ocean EX's opening, but that's an anime and not a video game so...