Roman Surface
An immersion of the projective plane with 4 cross caps
Boy's Surface
An immersion of the projective plane with 1 triple point
Cayley's Cubic
x^2+y^2+z^2
+4 x y z=1/4
Dupin's Cyclide
Hunt's Surface
Bohemian Dome
Envelope of a circle rotated about a circle. Thanks to John Ckertok for this.
Bohemian Star
Diagonal surface of Clebsch
A cubic with 27 straight lines
Cassini's Surface
Miter Surface