Classic Klein bottle. Part of my motive for making it was to see whether I could make a graceful shape from a single set of parametric equations, rather than patching together pieces of several different tori.
Lawson's surface, by stereographic projection from the hypersphere.
w = cos(u) cos(2v), x = cos(u) sin(2v), y = sin(u) cos(v), z = sin(u) sin(v)
A "Klein bagel": a figure-eight sweeps in a circle while making a half-turn around its midpoint. Alternatively you can think of it as what you get if you bend the edge of a Möbius strip over so that it meets itself in the middle.
Box of ellipses: x = cos(t+α), y = cos(t+β), z = cos(t+γ), where α is a multiple of 2π/3, β is a multiple of 2π/5, γ is a multiple of 2π/7.