Freeware
MTV Grabber is a freeware program that can record flash videos from MTV.
I've tried version 4.05 and was able to download RTMPE flash videos from mtv.com. The program doesn't seem to work on mtv.co.uk, mtv.ca, mtvu.com,...
The paid version of the program called
save2pc Pro + Extra Pack supports more web-sites, but from all MTV web-sites I was able to download from mtv.com only.
See also:
RTMPE stream recording/downloading/capturing/ripping/saving