You might be interested in Michael Artin, Barry Mazur: Etale Homotopy. Lecture Notes in Mathematics 100, Springer-Verlag 1969.

See also http://epub.uni-regensburg.de/14043/1/MP101.pdf and http://archive.numdam.org/ARCHIVE/PMIHES/PMIHES_1973__42_/PMIHES_1973__42__5_0/PMIHES_1973__42__5_0.pdf