Electrolysis is very important for generating and separating pure elements from compounds.

One important example is creating hydrogen (and oxygen) gas. Hydrogen gas is a potential future fuel for energy storage and powering vehicles. One way to make hydrogen gas is with the electrolysis of water

Electrolysis is used to extract and purify many elements from ore including aluminum, lithium, sodium, potassium, magnesium, and calcium. It can also be used to produce chlorine gas, sodium hydroxide, perfluorinated organic compounds, and many other elements and molecules.

Anodizing metals is another use of electrolysis. In anodization, electrolysis of an aqueous acid solution or organic acid is used to oxidize the surface of a metal in order to create a passivating oxide layer. This layer prevents the metal surface from being corroded

A related process, electroplating is used to coat metals with another type of metal from solution. For example, instead of making an object out of pure gold, it could be made with a less expensive metal and electroplated with gold.

References:
http://en.wikipedia.org/wiki/Electrolysis
http://www.britannica.com/EBchecked/topic/183116/electrolysis
http://en.wikipedia.org/wiki/Anodization