Here's Quentin Tarantino's take:
"A good majority of the cues in here, I had in mind in the writing stage. I don't add them to the script because then they ask for more money. If I usually put anything in the script, it will be the wrong song. Then we say, "You're really the second choice, you know, because we really wanted The Judds!" A good majority of them I come up with beforehand. More or less the way my method works is you have got to find the opening credit sequence first. That starts it off from me. I find the personality of the piece through the music that is going to be in it. If there is going to be no modern music in the movie, then that becomes the personality of the piece, but if there is, it is the rhythm that I want the movie to play at; it is the rhythm of the film. Once I know I want to do something, then it is a simple matter of me diving into my record collection and finding the songs that give me the rhythm of my movie. "I find the personality of the piece through the music that is going to be in it."

Although not every writer gets as much control as he seems to have, he seems to have music in mind even though he doesn't put it in the script and in some cases he lets the music set the tone for the scene instead of finding music to fit the mood.

Thanks, Kyle. I'll promote your comments to the OP as there's absolutely nothing wrong -- and in fact a good idea -- for a writer to keep a song in mind as inspiration when writing a scene, character, story, etc.

Another thought: perhaps the writer can make song style suggestions (slow rock, upbeat reggae, etc.) or even name the types of rhythms they had in mind while writing the scene. That way, the studio can choose the actual artist and song, but the writer can still influence the style/feel of the music in a scene.

@Gregaria: Absolutely a writer can do that. I should have mentioned that in the first place. Thanks!

What if my script takes place in Salt Lake and I actually know the bands locally I want to use?

@Nicholas: Unless the bands are hugely popular, then you're dealing with another situation: Why would you include a song title for a song a script reader would not likely know? Perhaps there are actual lyrics you want to use tied to the story's theme. But if the songs have been recorded and are for sale, you still have to go through licensing issues in order to get the movie distributed, even if it's just a small independent film.

That makes sense. I'm just planning on going punk rock and filming this thing myself. However, in keeping it professional I'll just pencil in the potential songs on my personal draft.

Thanks for the reply.