I think it's a Lockheed C-119, very cool plane, decent movie too!

Actually it's a C-82

A C-82 was used in the 1965 original; the remake made use of a C119.
Here's a link to info on the real aircraft used in both films...
http://www.uswarplanes.net/specialfeature.htm



I haven't seen the remake, but the 1965 original is superb, and unlike the remake, it featured an airworthy Phoenix (the second production ran out of time and money, and couldn't complete a flying full-size one). Legendary stunt pilot Paul Mantz died when the Phoenix crashed during shooting of the original film.
And not to be ghoulish, but here's a link to stills from the footage of the last  flight of the real Phoenix- I couldn't find any other pics of it in flight, other than the original movie itself. Only a tiny piece of this film was used in the final cut.
  The story of how Mantz, and not his partner, wound up making that fateful flight is pretty chilling... fate is the hunter, indeed. Submitted with all due respect to the incredible Mr. Mantz, who was nothing less than a master artist of flight. Charles Lindbergh's quote at the bottom of the page sums up the essence of a guy like Mantz pretty well. He lived a long life for such a bold pilot, and he died happily fulfilling his true calling...
http://stripe.colorado.edu/~steinerd/Phoenix.html


And, BTW, you might be interested in this (scroll to bottom of the page):

http://www.planesimulation.com/fsdownloads4/FS4a1x19.htm