The following uses for zirconium 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).
The metal is used in the nuclear industry for cladding fuel elements since it has a low absorption cross section for neutrons. Zirconium is very resistant to corrosion by many common acids and alkalis and by sea water. It is therefore used extensively by the chemical industry where corrosive agents are employed. The metal is used as an alloying agent in steel and for making surgical appliances. The metal superconducts at low temperatures and zirconium/niobium alloys are used to make superconductor magnets. Alloys with zinc become magnetic at temperatures below 35 K. Zirconium is used as a "getter" in vacuum tubes, in flash bulbs for photography, in explosive primers, and in lamp filaments.
The oxide (zircon) has a high index of refraction and is a good gem material. The oxide is also used for laboratory crucibles that will withstand heat shock, for linings of metallurgical furnaces, and by the glass and ceramic industries as a refractory material.