For instance:

- A point, line, and a sphere all have genus zero
- A torus has genus one, as does a coffee cup as a solid object (solid torus), a Möbius strip, and the symbol 0.
- The symbols 8 and B have genus two.
- A pretzel has genus three.

In algebraic geometry there is a definition for the genus of any algebraic curve *C*. When the field of definition for *C* is the complex numbers, and *C* has no singular points, then that definition coincides with the topological definition applied to the Riemann surface of *C* (its manifold of complex points). The definition of elliptic curve from algebraic geometry is *non-singular curve of genus 1*.

in graph theory, the genus of a graph is a integer n such that the graph can be drawn without crossing itself on a surface with n-handles. Thus, a planar graph has genus 0. (can be drawn on a sphere without self-crossing)