This has been added in 10.7 (albeit by a slightly different means):

"Command-C" then "Command-Option-V" will remove the originating file.

I actually like it better; you get to decide how to treat the files when the operation is actually executed, not when you initiate it. This negates the need to go back and remove the files when you realize you meant to Ctrl-X instead of Ctrl-C.

A source: http://osxdaily.com/2011/07/29/cut-and-paste-mac-os-x-lion/

(And to the other replies: he means in Finder. Cutting files hasn't been possible prior to 10.7)

Yes, "Command-X" handles that case. Pretty much every editing shortcut from Windows converts over by using command in place of ctrl. Though I couldn't state that that's always been true, it has been as long as I have used Macs (late '06).

Yes, there is a cut/copy/paste (CMD+X, CMD+C, CMD+V).

There was a time (don't recall which iterations) in which the MAC OS finder didn't support those three for _files_ - but I think they've always worked for images/text/etc...