Should I just move on if a professor doesn't answer my emails requesting a letter of recommendation? I've asked a professor who I did research with over the summer to write me a letter a recommendation for graduate programs, but he hasn't responded for over a week. I've resent him an email and have received no answer, but a peer who also worked in his lab over summer got an almost immediate response when asking for a letter. We have both done the same research in his lab and known him for the same amount of time. I don't mind if he declines, but I haven't received any word from him. Should I just move on and ask another professor?
Stop by his office (if in town) or pick up the blower.  Just ask him directly if he'll do it or not.  A lot of people are not so email/text centric.  He'll either say yes or no, but at least you'll know the answer.  (And if he says no, just drop it and move on--don't argue.)  

Personally, I wouldn't cross off and move on, just because of not responding to email.  Especially if he's the best one.  He is probably just busy.  Or a procrastinator.

Voice or face to face are direct.  An email is like a letter.  Easy to ignore, to get to it later (which becomes never), etc.

When you do confront him if he says, he's unsure of what you did, offer to give him some bullet points and a BRIEF explanation of what you're going after and key features to emphasize.  (In the nature of making his job easier.)