I orignally began this as a response to Kelly's post, but it grew enough that it seemed to warrant becoming a separate post of its own.
As Kelly says, I tend to leave my first draft alone as it takes form. This is mainly for the simple reason that if I went back to "fix" things, I would never get beyond chapter three. I would fix, and re-fix, and re-re-fix forever. For me, it is push on to the end, then go back and straighten out whatever train wrecks may have happened along the way.
The first main exception to this is if I come to a point in the story where what is happening on the page now requires major changes to what has come previously. Even then, I may simply make a note in my Revision Notebook, adjust the outline, and keep pushing on. Or I may go back and rework the last 200 pages. But unless that latter is absolutely necessary, I try to do the former.
Ideally, of course, this kind of mid-story revision shouldn't happen since I outline, but I tend to put equal empahsis on plot and character. This means that one can serve the other, or vice versa, depending on where I am in the story. Plot usually over-rules character, but I find that isn't always the case.
The second exception to not going back is my habit of sometimes revising the last two pages I wrote before moving ahead. That mainly happens if I am stuck, or really not happy with what came before. The main focus, though, is always on moving forward.
Overall, I tend to be fairly generous with myself when it comes to the first draft (the phrase "kitchen sink" comes to mind :). However, in the second draft, I approach the MS with a gleam in my eye and machete in my hand. It may be more work than following a harder outline like Kelly does, or revising on the fly like both Kelly and Lyda, but it's the method that I am most comfortable with at present.
As to for Erik's comments on what to cut: well, part comes from feedback from the Wyrdsmiths (although I don't always listen to them :); part comes from my gut (does something feel right?); and part comes from cold, hard analysis of deciding if a scene/action/sub-plot really serves a core purpose. If it doesn't advance the plot or tell me something important about the character that we don't already know (and is relevant to the story at that point in the book), it shoud probably go.
Caveat: The above goes with the understanding that other people may have other core purposes when making revision decisions, depending on their focus. If a person is more of an idea writer (the story is there to hang a cool concept on), then the focus may be on the scene presenting another facet of the central concept; if they are more of a world builder, then pieces that further illuminate the depth of setting may need to stay; if they are a hard science writer, then the nuts and bolts of how things work may be critical. What I consider core is what is most important for my story, but may by no means be a critical consideration in another author's process.
Ultimatley, drafts and revisions, IMO, are all about making the story stronger. The tricky part is developing the craft to figure out just what will accomplish that. And that learning curve never ends.