This is in the PC gaming section but it really applies to all platforms.
In the past year and a half now since I joined the PC gaming scene I have played quite a lot of indie games as well as some bigger titles. Many different genres, styles, mechanics, and atmospheres, though the music and sound in the games always seem more prevalent to me than the visual aspect. There have been a few cases so far in which I found myself liking a game more than I would have otherwise because I enjoyed the audio. Playing a game with somewhat bland mechanics is made altogether that much better because of the music and sound; specifically, Superbrothers: Sword & Sworcery, Super Hexagon, and Proteus to name a few. To me, the audio is the most important reason why I enjoy a game.
Sword & Sworcery is a game where you walk around, look at stuff, solve a few puzzles, and fight a few enemies. Not all that much is actually going on when you are solving the puzzles. Walking around is kind of boring but not when listening to Dark Flute or Lone Star, by Jim Guthrie, from the soundtrack. The battles with the Gold Trigons are epic solely because of the track that plays during those fights. Aside from the beautiful art style, the music itself made the game one of my favorites.
Imagine how long you would play Super Hexagon if it had no music. It would have the same mechanics and visuals, but it would be a lot less interesting if those upbeat chiptunes were removed. I have turned off the music before and, while it may actually help in beating a level, the game just feels lifeless without it. The games does have some replayability because of the difficulty but this title is one I've put over twenty-five hours into. The music added that much replayability.
Proteus is a game where you walk around and look at the environment. That is all. Normally I would have passed on the game but after playing it for a few minutes and noticed how the world reacted to me via the music changing actually gave the game more replayability than it initially had. Not to say I played the game that much, I actually did go back a few times to the game because of the dynamic soundtrack.
There are a lot of other titles I feel that do music and sound incredibly well, like FTL, Risk of Rain, Bastion, and The Swapper, to name a few more. Even Planetside 2's long loading times are made tolerable with its loading screen music. Red Orchestra 2 makes every event during a match feel like it has an impact with the accompanying music.
Now that my reasoning is explained, how much do you value the audio in video games? Does it make or break a game for you?