Super important. I don't think I'd be nearly so infatuated with the Ys series if it weren't for Yuzo Koshiro's music.

Do you even imagine Chrono Triger or Cross without Mitsuda's soundtrack?

Nope, especially for the latter. I wouldn't have played the game if it wasn't for the music.

Yes, music can force me to finish a game. I guess it's the only thing that does it!

A good way to show how important music is to a game.

Try playing a game with no music.

It sets the mood of the game.

Games with good music are usually good games.

Games with bad music are usually bad games.

Unfortunately great OSTs aren't usually found in video games.

 I find this a bit silly.

Gameplay. What is that? How the game plays? It's far too large to be a category.

Graphics? Do you include physics, AI and all of that? If you do, you're bloody insane if you put music above it. If you don't, where the heck did you put it?

I think game music is integral the to gameplay experience. It's very, very important.

Also, I may as well mention that I'm an avid collector of VGM.

if it wasn't for the music final fantasy wouldn't be so popular nowadays.
each time they announce a new final fantasy the first thing that comes in my mind is that awesome music .can't wait to hear FFXIII and vs XIII soundtrack.

That's totally truth... although I would find better samples (somehow I have some problem with Uematsu... he's good, I would never say the contrary... although I think he's overrated, and although the best on the technical side, it lacks some feeling).

A good music in a video game should be the one we don't even notice is there (unless we really want to notice it, of course). It simply sounds natural. And in most Final Fantasys, that happens.

Good music can really set the mood in many games. So to answer your question it is very important to me.