Why do PCBs always have an even number of layers?
It's possible to make multilayer boards with odd numbers of layers, but they are non-standard, there is no cost savings and there is another issue- the asymmetrical stack-up will tend to lead to excessive warp and twist, particularly after soldering.

The stack-ups are made from cores with copper on each side, separated by pre-preg insulator, so they naturally come on pairs. It's better to add another routing layer or ground plane than to use odd layers.

Edit: As Brian and others have pointed out, single-layer boards are an exception. Presumably because the foil layer is on the outside of a relatively thick laminate core they do not seem to show so much tendency to warp (though I've had problems with large paper-based phenolic boards after wave soldering). Single layer boards are used in huge quantity for such things as power supplies (where the component density is low and dominated by the large components and clearances required) and disposable consumer goods (where punched boards are de rigueur to meet the price point).