What is the best way to backup pictures and music on your hardrive?

I was looking at flash drives, external hard drives and paying a service online to backup. Which is best?

burn them to dvd as data.

for speed the external hard drive - but hard drives can go wrong - the web service can take a long time depending on your internet speed, but this will never fail as the service will have failure contingency - i'd say use the external hard drive - get one with a network port so it can be setup as a standalone device if needed (it will also have a USB port) i'd also make backups using DVD's as an extra precaution.