Famous Viennese architect and artist Friedrich Hundertwasser was invited by the City of Vienna to design a living space in his own style. Respecting the arbitrary lines and curves of nature, the resulting house is a multicoloured monument to Hundertwasser's inimitable style. Very much worth a visit.
Corner of Kegelgasse and Lowengasse;
www.hundertwasserhaus.at/HwH/en_main.htm
But it's worth noting that you can't go inside. You can only view the house from the street.
There's also a museum KunstHausWien dedicated to Hunderwasser at Untere Weißgerberstraße, 13. Museum, galleries, lovely cafe all with characteristic multicolours and wobbly floors. Also features the Toilet of Modern Art.