What % (and #) of the american population has at least one health care
encounter/visit in a year? (i.e., went to doctor, ER, clinic,
hospital, etc.)

84% of the United States population (239,090,014 individuals) had at
least one health care visit in 2004 (the most recent year for which
the National Center for Health Statistics has compiled statistics on
this subject).

In 2004, 82% of American adults and 90% of American children had
contact with a health care professional. In 2004, the total population
of the United States was 284,570,767. The adult population was
212,795,958, and the child population (unter age 18) was 71,774,809.
174,492,686 adults and 64,597,328 children had health care visits in
2004, for a total of 239,090,014 individuals. This amounts to 84% of
the U.S. population (of all ages).

Additional details, and a breakdown of the data, may be found here: 

National Center for Health Statistics: Ambulatory Care Use/Physician Visits
http://www.cdc.gov/nchs/fastats/docvisit.htm

NCHS: Ambulatory Medical Care Utilization Estimates for 2004
http://www.cdc.gov/nchs/products/pubs/pubd/hestats/estimates2004/estimates04.htm

I obtained the U.S. population figures for 2004 here:

Food Research and Action Center: United States
http://www.frac.org/State_Of_States/2006/states/US.pdf

My Google search strategy:

Google Web Search: site:cdc.gov percent "medical care"
://www.google.com/search?hl=en&q=site%3Acdc.gov+percent+%22medical+care%22

I hope this is precisely what you need. If anything is unclear or
incomplete, please request clarification; I'll be glad to offer
further assistance before you rate my answer.

Best regards,
pinkfreud

Thank you very much for the five stars and the nice tip!

~pinkfreud