Also atelier iris 3 the grand phantasm has a great intro

"I had a dream that I could fly"

Maybe not my all-time favorite (there are too many to choose from), but I will never forget the first time I launched Rocket League during a Steam free weekend. Back then they had Breathing Underwater as the main theme and the way the logo appeared in sync with the music was such a beautiful sight.

I linked the high quality song above, but if you want to experience exactly what I did, here's a link to a video with the intro captured from the game. Still gives me goosebumps when I see it.

Needless to say, I bought the game.

Probably the sting in the original Street Fighter II

Though there's a sort-of full version in MvC as Ryu's theme

A lot of games don't even have menu music anymore, or it's ambient and not really noticeable....

Lagoon (SNES), Premonition, such a banger.

Baldur's Gate II

(honorable mention - Civ IV)

Haven - The Beginning of Something.

Whole OST is pretty good.

Off the top of my head, either Ecce Valde Generous Ale (Behold the Precious Wings) from Panzer Dragoon Saga or the one in Trails from Zero.

https://www.youtube.com/watch?v=QlP3eE9Vlg8&t=6128s

IXION is definitely mine. If you skip through that video a bit, you can hear some more music when the Prologue begins to play. Such an amazing game!