Are there any publications that were motivated by a CrossValidated post? Was the site acknowledged? Is there a badge for that?
I thought that the answers to the question "For which distributions are the parameterizations in BUGS and R different?" would be of general interest to the R community so I wrote it up (in collaboration with the answer's author). The article "Translating Probability Density Functions: From R to BUGS and Back Again." is methodological, though the research part was limited to compiling references.
The acknowledgements read "This collaboration began on the Cross Validated statistical forum (http.//stats.stackexchange.com/q/5543/1381)."
Hopefully there will be at some point. I am performing an empirical study of Nelder-Mead simplex, gradient descent and grid-search methods for model selection for kernel machines, which was inspired by a question on Cross Validated (which appropriately is also the model selection criterion ;o). No paper yet though.
A badge for it would be tricky, as it's not an automatic thing that can be scraped from the site itself.
I don't know of any methods research spawned by CV, but I haven't been here all that long, so someone may come and chime in. I have however used it to sanity check an idea or two that I've had. Though the one time CV did out-and-out answer the question, I had a better source provided.
Almost two years after having asked this question, I actually wrote a paper inspired by CV (still unpublished):
I used the question's url in the body of the text.