Originally Posted by el_duderino

Fuses have two purposes:

1) To protect the device at the end of the wire. This is sometimes impossible, since if the thing starts pulling more juice it might mean it's already gone, but with amplifiers it's often beneficial. It also protects the device from catching on fire hopefully if it develops a bad internal short.

2) To protect the wire and by extension the car. If the thing does short out, we don't want it pulling so much current that the wire catches on fire. Also, when we add wiring to a car, we know that it's not always in as protected a routing location as a factory wire, so we want to be sure that if the wire gets pinched to ground or gets a screw through it or something violent like that, the fuse pops, instead of the wire going smokee-smokee.

Your DVD player might have an inrush of current when loading or ejecting. 5A is probably not a bad call, but make sure that it's enough for those current-peak conditions.

Remember that for a fuse to blow it's usually not instant. Read this for more info on a graph:
http://www.bussauto.com/pdf/atc.pdf