\[ (x^3-1)^2+(y^3-1)^2+(z^2-1)^3 \]
- degree 6
- four singular points, smooth otherwise
I just love the way this surface looks. From the raytrace on Herwig Hauser's gallery, it's clear the surface has at least four singularities. And that's just how many it has. They occur at (1,0,0), (0,1,0), (1,1,1), and (1,1,-1).