What is the melting point of diamond?
Diamond (carbon) does not melt at 1 atm. It sublimes to vapor.

Using carbon's theoretical phase diagram below (from Wikimedia), "liquid diamond" could be achieved at about 10 GPa (99 thousand atmospheres) and 5000 K (4700 °C).



Edit:

In fact, heating up diamonds at 1 atm turns them into graphite first. Only further heating would cause sublimation, as expected by observing the phase diagram. Here's a video:

http://www.youtube.com/watch?v=7L7BV3IBfFA