Hate to answer my own question, but I managed to find my references :-).  In case anyone else is interested in this, these are useful, and other more would be appreciated:

- Diaz JA, Griffith RA, Ng JJ, Reinert SE, Friedman PD, Moulton AW. Patients' use of the Internet for medical information. Journal of General Internal Medicine 2002;17:180-5.

- Diaz J, Sciamanna C, Evangelou E, Stamp M, Ferguson T. Brief report: what types of Internet guidance do patients want from their physicians? Journal Of General Internal Medicine 2005;20(8):683-5.

- Delic D, Polasek O, Kern J. Internet health-information seekers in Croatia--who, what, and why? Medical Informatics And The Internet In Medicine 2006;31(4):267-73.

- Hay M, Cadigan R, Khanna D, Strathmann C, Lieber E, Altman R et al.. Prepared patients: Internet information seeking by new rheumatology patients. Arthritis and Rheumatism 2008;59(4):575-82.

- Klinar, I. et al., 2011. Identification of general characteristics, motivation, and satisfaction of internet-based medical consultation service users in Croatia. Croatian medical journal, 52(4), pp.557–565.

My own experience is less than 1%, but I don't have any kind personal research.

Just to clarify, though, I'm not asking what percentage of patients look up information on the Internet.  (That figure is high, as some studies show, but it does fluctuate across population groups, regions, and is heavily impacted by education, etc.).

The question I'm looking at is this:  Of the patients who look up information on the Internet, what percentage DO NOT tell their doctors about what they have found?  I think that, by very definition of the problem, a doctor would not be able to answer that question just by asking his/her patients, because, if they don't tell, then they don't tell.

This is a very real problem, because the research suggests that the figure is as high as 60-80%.  So, why are patients not telling their doctors?  and what are the patients doing with this information?  What does this figure say about the overall patient-doctor communication going on?  Is medical communication all just a one-way street?

Thanks for your response.  Yes, it's actually part of a larger area of research of mine, the e-patient. (Patients who are engaged, and use the Internet to find information).  As you describe, some (many?) doctors are not keen on that equal patient-doctor communication, but it can have tragic results.  I have a short paper on such a case at: http://www.tandfonline.com/doi/full/10.3109/0142159X.2015.1112896

Thanks for taking up this theme for discussion. This theme is quite relevant in today's context. The medical fraternity is aware of a good number of patients who come quite prepared to show themselves in a hospital/clinic. The patients are much more knowledgeable now than before, thanks to internet. It is a very good to have equal patient-doctor communication. On rare occasions it starts appearing that patient is trying to test the doctor's knowledge on the subject! That is why It is always good to be better informed, read and educated than patients. I am interested in your research Ken! All the best!