Will withdrawing from a graduate program, affect my future admissions applications? I am in an MS program at a big university in the US, where I pay my own tuition. 

I am not happy with the quality of education I am getting at this university.

I am thinking that after this quarter is complete, that I want to officially withdraw from the program and go somewhere else. I think I can get much better education and for much less cost as well. 

My question is: Will this affect me in any way for future admission to other schools? I am an A student, and I'll be withdrawing after the quarter is over, not in the middle.

Will the transcript contain some negative marker in it because I did not complete the MS program?  Has anyone been through this and found any negative effect when not completing a program?
Your transcript will very likely have a notation that shows you withdrew from the program; to claim that you are still enrolled when you are not would be dishonest (if either you or the university said so!).

And yes, this will be something that you will need to explain to schools to which you apply in the future. Just saying "it's not good enough for me" is a bad reason to withdraw from the program, because it suggests a "diva-like" attitude that is not particularly desirable (in just about any circumstances). If you're responsible for paying your tuition, and found you could no longer afford it, that would be a more tolerable reason.

But you will need to explain this, and it can definitely have an impact on the decision of future admissions committees.