The following uses for tantalum are gathered from a number of sources as well as from anecdotal comments. I'd be delighted to receive corrections as well as additional referenced uses (please use the feedback mechanism to add uses).
Tantalum metal has a number of important uses. It is used to make steels with desirable properties such as high melting point, high strength, good ductility. These find use in aircraft and missile manufacture. It is very inert and so useful in the chemical and nuclear industries to line reactors. Tantalum wires were those used first for light bulbs (now tungsten is preferred). The metal is immune to body liquids and the body tolerates the metal well. Therefore, tantalum has widespread use for surgical use. For instance, it can be used in sutures and as cranial repair plates. The metal is used in the electronics industry for capacitors.
The oxide is used to make special glass with a high index of refraction for camera lenses.