If you're fortunate enough to have a good critique group or first readers, you're going to get a lot of advice on your work, some of it spot-on, some of it close to the mark, and some of it that you violently disagree with. (If you're not that fortunate I'd strongly recommend doing something about it as you'll learn a lot both getting and giving critique).
The spot-on stuff is easy. You just do it. The close is also pretty easy, as it can be adapted to fit. It's the violently disagree with that's hard, because as much as you might like to, you shouldn't just dismiss it.
Readers offer suggestions because they either disagree with the choice you've made, they've missed something you expected them to get, or they've gone somewhere you didn't expect. In all of those cases, it's important for you as a writer to understand why that happened and whether it's because you didn't put something that was in your head down on the paper, because you've left something sketchy where you should have filled in the details to keep your reader on the path, because you didn't think of it, or simply because your reader has missed something obvious--it does happen.
The process I go through when I've been handed a suggestion that seems to me to come out of left field is thus: 1, put it aside for a moment to see if my backbrain can field the ball and figure out what went wrong. 2, Wait to see if anyone else had the same problem/suggestion or one that came in the same place. 3, ask questions of the critquer.
That last should be handled delicately. The person making the suggestions is giving of their time and perspective and you owe them the courtesy of being both polite and respectful no matter how wrong-headed you might think this particular comment is. You're not trying to defend whatever they've disagreed with, you're trying to find the root of the disagreement.
I try to ask questions like, okay you've said X, can you expand on that a bit? Or, if I've got an inkling what's wrong, here's what I was trying to do there, did that come through? Or, sometimes, what if I told you x about what's coming up, would that change things?
This is one of the places where the Wyrdsmiths really excel--often, while I'm still trying to figure out what lost someone, another person in the group who has better perspective, figures it out and gives me the piece I need to make sense of the critique, or better still, proposes a solution that fits into the spot-on frame, thereby saving me a ton of work.
Of course, sometimes it comes down to artistic or philosophical differences about where a story should go, and there you have to be willing to say X is going to make some percentage of my readers unhappy and accept the consequences, whatever those might be. It's not much fun, but it's what owning your work means.
So, how do you all deal with the comments that make you scratch your head or clench your fists?
Update Elizabeth Bear has a link to a post on editorial letters at Blue Rose Girls that's relevant to the topic at hand.