Should I keep my name on a paper in which I have no important contribution? Prof. X added me as a coauthor on a paper , although my contribution was minor. I told him so, he insisted and said it was necessary for me (I can't give details). Later my relation with Prof X seriously soured. I asked that he remove my name from the paper: I already have an OK publication record (about 100 citations) and I didn't want to pollute it with an undeserved paper, especially in view of the souring of my relation with Prof X.
I had an essential contribution in all my previous papers. Prof X said it was impossible to remove my name since it was already submitted. I reluctantly accepted. The paper was rejected. Prof X wants to resubmit it to a less prestigious journal. I definitely don't want my name on it. Prof X insists to keep my name, saying that re-submitting the paper without my name might harm his reputation in the community. I can't claim to be white as snow : It's clear that I should never have accepted to have my name on this paper in the first place. I don't want to antagonize him further, but what should I do now ? Is it true that resubmitting without my name can harm his reputation ? Isn't there some way around this ? (My field is Math/Physics/Engineering. I can't give more details).
Standards (and customs) for coäuthorship depend heavily on your field, but if you contributed to the work reported in the paper, you might first want to consider actually accepting coäuthorship:


Unless you think the work is actually crap, there is no downside (having a few not-so-great papers doesn't actually hurt, even if it doesn't help your career).
If you worked with prof. X, it might be nice to have something (a paper) to show for it.
The relationship may have soured, but are you ready to burn that bridge? If he insists on coäuthorship, a flat refusal will annoy him, probably because it would hurt him for some strategic reason.


Now, on the other hand, it's entirely your choice to make. Nobody can force you: if it comes to that, just flatly state that you do not wish to be a coäuthor on the paper. After that was made clear, and in writing, there is little chance prof. X will submit it with your name behind your back: that would be a very severe breach of ethics, and grounds for immediate retraction of the paper when you find out.

Finally, on the question of whether resubmitting without your name can actually hurt him… yeah, it could be an annoyance. There are a few people (editor and referees for the first paper) who would have knowledge that the same paper was submitted twice with different author lists, which definitely gives a bad impression of the senior author.