If Erdős is published as Erdös in a paper, which do I cite? There seems to be a few papers around with Erdős written as Erdös.  For example:
MR0987571 (90h:11090) Alladi, K.; Erdös, P.; Vaaler, J. D. Multiplicative functions and small divisors. II. J. Number Theory 31 (1989), no. 2, 183--190. (Reviewer: Friedrich Roesler) 11N37

Would it be incorrect to cite such papers using Erdős instead?

 A: 
A proposed compromise
A: My rule of thumb is to spell names as MR spells them. I just looked up Erdos in MR, and it turn out that there is a Paul Erdös as well as a Paul Erdős (different people). Since you mean the second, you should spell it correctly, or else put (sic) in your bibliography. 
A: This is a matter of convention.  One guideline is in paragraph 17.20 of the Chicago Manual of Style (15th ed):
Authors' names are normally given as they appear in the title pages of their books. Certain adjustments, however, may be made to assist correct identification (unless they conflict with the style of a particular journal or series.  First names may be given in full place of initials.  If an author uses his or her given name in one cited book in and initials in another (e.g., "Mary L. Jones" versus "M. L. Jones"), the same form, preferably the fuller one, should be used in all references to that author.
I would err on the side of consistency.  Some bibliography styles in LaTeX/bibtex replace subsequent references to the same author with an em dash.  If you use many different spellings of the same author's name, this behavior will break.
A: We cite papers to show our respect to the authors and to help our readers find stuff. For the second purpose, I suspect most people would just type in names without diacritical marks, and most search facilities would find what you're looking for based on the letters alone, so it doesn't really matter. But for the first purpose, I think you should spell the name the way its owner would want it spelled, regardless of what some journal may have done. 
A: Cite as it is in the journal. Are you absolutely certain that you know how the author wants his/her name spelled? Are you absolutely certain that the person you think is the author is the author, and not somebody else with the a similar name? Accents and spelling can change or be dropped when a person emigrates or to conceal an ethnic origin, and sometimes that is what is preferred by the person.
A: In response to Gil's compromise (because you can't put images in comments apparently), you can get the desired effect with \textdotacute from the tipa package from CTAN.

;-)
