Who is the actor that plays Big Bird on Sesame Street (i.e. the voice
and person in the costume)?

The actor's name is Caroll Spinney.

  - The Official Caroll Spinney Fan Page
   ( http://carollspinney.netfirms.com/ )

From the Odiecus  - Trivia Entertainment page
( www.geocities.com/odiecus/cosasinteresantes/ingles/triviaentertainment.htm
)
 "In Sesame Street, one man, Caroll Spinney, plays Big Bird AND Oscar
the Grouch. From within the 8' 2" yellow feathered suit, Spinney
watches a small monitor with the same view as the audience. He
operates Big Bird's head with one hand while working bird's hand with
his other. When Oscar and Big Bird are in the same scene, Spinney
speaks for both Muppets, while another puppeteer operates Oscar. "

:)