Thought the Möbius band was divine.
Said he: "If you glue
The edges of two,
You'll get a weird bottle like mine."
This Instructable will teach you how to make a Klien bottle, which is a bottle with no distinct inside or outside; a non-orientable surface. You can read more about them here and on Wikipedia. A Klein bottle is very similar to a Möbius strip, the difference being, to quote Wikipedia, that "Whereas a Möbius strip is a surface with boundary, a Klein bottle has no boundary".
A real Klein bottle could not exist in 3 dimensions though, as it passes through itself without leaving a hole. This is not a "real" Klein bottle, because it cannot exist in our world. This is merely the 3 dimensional expression of the impossible shape.
We have, however, figured out how to rotate a four dimensional object through its dimensions, and a good demonstration of that can be seen here, however I can't seem to find a video of a Klein bottle being rotated through it's four dimensions.
There are alternate versions of the Klein bottle like the "figure-8" shape, or the "Lawson-Klein" version, but in my mind they do not hold as much water as the classic Klein.