A torus can be cut into one with an even number of half-twists and a Klein bottle cut in half makes two of these.  
Any non-orientable surface contains one.  It contains one boundary curve and cannot be embedded in the real plane.  A torus can be cut into one with an even number of half-twists and a Klein bottle cut in half makes two of these.  B.F. Goodrich supposedly patented a conveyor belt in, for ten points, what form, theorizing that its one-sidedness would ensure even wear.
Any non-orientable surface contains one.  It contains one boundary curve and cannot be embedded in the real plane.  
Mobius strip (or band)