Tungsten (wolfram) is fun because it is the most dense metal you can find at a reasonable price. Tungsten is exactly as dense as gold. People just love to hold things made of tungsten. Because they are so darn heavy, they put a smile on everyone's face.
This is a privately minted pattern designed by Fred Zinkann for the 1987 Constitution Bicentennial commemorative. It was struck in various metals by Pressed Metal Products, Vancouver BC and is listed in Andrew Pollock's book, "US Coin Patterns". 88 were struck in .900 tungsten, Pollock #5465, and at least one has been certified by NGC. The tungsten strikes were all very weak due to the extreme hardness of the metal.
Fred Zinkann also made a fantasy issue in tungsten - a Kerguelen pattern - but the dies broke after the second or third coin was struck, or so the story goes.
http://www.usns.info/coin-kerguelen.html
The Inkling Pen Company used to make a tungsten medal to advertise their BOMApen. The medal has a nice design laser etched on it: the Boma, a Balinese protector spirit. The BOMAcoin sold for $180, but alas they're sold out now.
No circulating legal tender coins are made of tungsten.