Answer: Apollo 17 team
The photograph was taken by the Apollo 17 astronauts (Cernan, Evans and Schmitt) on December 7, 1972, at 05:39 a.m. EST. this was the first ever NASA mission that allowed for a full view of the earth from space as the astronauts had the Sun behind them when they took the image. It looked like a giant glass marble and hence it was named the Blue marble.
Since then, many photos of the Earth have been taken, but what makes this one special is that it was taken by humans. Apollo 17 was the last human flight into space and hence all photos taken since then have been via unmanned space craft.
Image credit: Public domain, NASA,Wikicommons