A fuse is designed to limit the flow of electricity through a circuit. However, in practice, many folks end up letting the wire act as a fuse due to bad installation. When a wire that is too small for the current going through it is installed, it can melt. A melted wire is the same in practice as a fuse, but you have to hunt it down. Generally the point of a fuse is to be the weakest point in the circuit. If you select bad wires, the logic doesn't quite work out.
Melting wire can cause some catastrophic failures, including but not limited to arcing, fires, melting plastic, rubber, and more! Generally you want to size the wires going through a circuit based on a separate series of equations. Please go here to get basic calculations for wire sizing. However, to ease the discussion, we have provided a list of maximum amperages across wire sizes. These amperages are for reference only, please have a qualified electrician do the math on your next big install to check your work.
American Wire Gauge
Recommended Maximum Fuse Size
Remember, these are the recommended maximum fuse ratings for the corresponding wire sizes. If you are using wire sizes smaller than the reccomendations with a larger fuse, there can be problems. However, using a smaller fuse than what is reccomended is the way to get an efficient system. Small fuse, big wire is always most safe.