The Map Folding Problem refers to the question of how many ways there are to fold a rectangular map along its (valley and peak) creases. (It's a companion of the Stamp Folding Problem, first described in 1891.)

For example : There are eight ways to fold a 2 × 2 map along its creases, counting each different vertical sequence of folded squares as a distinct way of folding the map.

However :

[…[ the general problem of counting the number of ways to fold a map remains unsolved. The numbers of ways of folding an n × n map are known only for n ≤ 7

Source : Wikipedia

Further technical information : Math. Comp. 22 (1968), 193-199