Would it be considered cheating to ask for homework help on the internet, if I openly acknowledge the help received? Say you have a homework assignment and you're struggling with it. You ask a question about some portion of it on a site like physics.stackexchange or math.SE or stackoverflow.com, etc.

You then cite the help you received in your homework, as well as including a link to the post which helped you.

Given that you are removing the "dishonesty" part of the equation, is this still considered cheating? Or would a professor just not give you credit for the part which they feel you didn't do on your own?
This depends a great deal on the professor and course in question.  Better to ask first if you plan to do this.  Also, check the syllabus if there is a stated policy regarding help on homework.