About Zircon

Zircon makes a nice gem but it's out of favor these days.
Zircon-zirconium silicate or ZrSiO4-is a hard stone, ranking 7? on the Mohs scale, but other stones are harder and its colors aren't unique. Tradition has a slim dossier on zircon; one site says that it was reputed to "aid sleep, bring prosperity, and promote honor and wisdom," but hey, just having the money to own jewels is good for that. It does have some minor mineralogical distinctions. It's the only gem in the tetragonal crystal class, for what that is worth. And it's the densest of the major gemstones, but that means a zircon of a given carat weight is smaller than any other gem of equal weight.
Maybe zircon can gain more respect if we look at its value to geologists. Zircon grains occur almost everywhere there are sediments, because the mineral is so tough. It rises through the crust in igneous rocks and is eroded into the stream system, washed out to sea, and laid down in the sediment beds where it becomes part of the next cycle of sandstone and shale-totally unaffected! Zircon is the ultimate geological recyclable; it can even endure metamorphism. That makes it a great indicator mineral. If you find it in a granite in one place, and in a sandstone somewhere else, you have learned something about the geologic history and geographic setting that brought the zircons from the first to the second place.
The other thing about zircon is its impurities, especially uranium. The uranium-lead (U-Pb) system of dating rocks has been refined to great accuracy, and U-Pb zircon dating is now a precise tool for rocks as old as Earth itself, some 4.6 billion years. Zircon is good for this because it holds these elements tightly.

Zirconia/Baddeleyite

Cubic zirconia or CZ is known as a fake diamond, but I think it should instead be considered a superior zircon. CZ is a manufactured oxide compound, ZrO2, not a silicate, and "zirconia" is a chemical name, not a mineral name.
There is a naturally occurring form of zirconia, called baddeleyite. The difference between baddeleyite and CZ is the way the zirconium and oxygen atoms are packed: the mineral is a monoclinic crystal and the gem is cubic (isometric), the same crystal structure as diamond. That makes CZ extremely hard-only diamond, sapphire, and chrysoberyl can scratch it.
The United States stockpiles over 14,000 tonnes of baddeleyite for its zirconium content. Like zircon it is useful for dating extremely old rocks, though unlike zircon its use is limited to igneous rocks.

Zirconolite

Zirconolite, CaZrTi2O7, is neither a silicate nor an oxide but rather a titanate. In 2004 it was reported to be even better for dating old rocks than zircon, yielding data as precise as the SHRIMP (sensitive high-resolution ion microprobe) instrument allows. Zirconolite, though rare, may be widespread in igneous rocks but not recognized because it resembles rutile. The way to identify it for sure is by using specialized electron microscopy techniques on the tiny grains before deploying the SHRIMP on them. But these techniques can derive a date from a grain only 10 microns wide.
The Geologist's Gem
To get an idea of what people can do with zircons, consider what researcher Larry Heaman did, as reported in the April 1997 Geology. Heaman extracted zircon (and baddeleyite) from a set of ancient Canadian dikes, getting less than a milligram from 49 kilograms of rock. From these specks, less than 40 microns long, he derived a U-Pb age for the dike swarm of 2.4458 billion years (plus or minus a couple million), just after the close of the Archean Eon in earliest Proterozoic time.
From that evidence he reassembled two big chunks of ancient North America, tucking the "Wyoming" terrane underneath the "Superior" terrane, then joined them to "Karelia," the terrane underlying Finland and adjacent Russia. He called his results evidence of the world's earliest episode of flood-bastitle volcanism or Large Igneous Province (LIP).
Heaman capped himself by speculating that the first LIP "could reflect either (1) the waning of a vigorous mantle convection regime that prevailed during the Archean and completely dissipated mantle plumes for more than half of Earth's history, or (2) the time of catastrophic collapse of a stable density stratification in the Earth's core that led to a sudden increase in heat flux at the core-mantle boundary." This is a lot to get out of a few tiny bits of zircon and baddeleyite.