Although I agree with Mr Remero’s answer (the plural of GPS is undoubtedly GPSs), I cannot agree with his statement about the apostrophe. The apostrophe has no place in forming plurals: GPS’s (or, indeed, GPS') would mean ‘of the GPS’, not ‘multiple GPS units’.

Even the Chicago guide recognizes that “mind your p’s and q’s” is standard usage. To say that this usage does not inform common practice with regard to pure acronyms is a little short-sighted based simply on the commonness of the “error.” Clearly using an apostrophe to form plurals is non-standard, but I can’t go so far in tone as to say it has “no place.” The meaning of the apostrophe, as with anything, is contextual and (gasp) may change according to context.

@Donald: According to Common Errors in English (http://www.wsu.edu/~brians/errors/apostrophes1.html) there is an exception: “in expressions where letters or numerals are treated like words, like ‘mind your P’s and Q’s’ and ‘learn your ABC’s’”.

My meaning of the term “pure style” is probably being interpreted as something like “it’s a free choice, do whatever you want.” What I actually mean is that for accepted/common usage and the regularization of printing practices, it is a matter of style. I am not saying, however, that this stylistic choice does not constitute clear usage standards, BUT you will notice that even Chicago hedges it’s bet so as to be open to choices that may avoid confusion. The only thing I take issue with is a harsh attitude about it. Using an apostrophe is an “error,” but I don’t see it as a jaw-dropping error.