One of the heavier "noble gases" (column 8A of the periodic table), Xenon has found widespread application as in strobe lights and extra-bright automobile headlights. (Xenon bulbs)
Originally thought to be inert, it is now well-known (as whort points out) that Xenon will form chemical compounds with reactive elements, most commonly fluorine and oxygen which are useful as oxidizing agents.
Perhaps the most interesting thing about Xenon is its apparent psychoactive properties. Although costs are still prohibitive, Xenon has been clinically shown to have anesthetic effects similar to nitrous oxide when inhaled (almost always in a mixture with oxygen). Possibly a dissociative, Xenon has been shown to be safer than nitrous oxide and most gaseous anesthetics in modern use due to its extremely chemically inert properties (as a noble gas.)
While costs continue to keep Xenon anesthesia from widespread use in the medical world, advances continue to be made in Xenon manufacture in order to make this useful (and unfortunately trace) gas more cost-effective in medical applications. The majority of xenon continues to be used in high-intensity light bulbs.