Is it possible to print a 3D printer?
It’s not currently possible to print 100% of a 3D printer, but you can print a good portion of the parts required, yes. http://Reprap.org has a lot more information.
The basic problem is printing the extruder - how do you print something that has to endure temperatures above the melting point of your material?
@Jason_McMullan The E3D folks actually played with printing PEEK, which would handle those temps.
Snappy RepRap is almost entirely 3D printed.
http://reprap.org/wiki/Snappy_3
http://reprap.org/wiki/Snappy_3