I think there is a very nice book by Huybrechts
Complex manifolds folder in Geometry. Many nice things, for example Global aspects of complex geometry.
http://mathoverflow.net/questions/4895/the-relationship-between-complex-and-algebraic-geomety
Larusson: The cat of complex manifolds can be embedded into a model cat in a way such that a manifold is cofibrant iff it is Stein, and fibrant iff it is Oka. See AMS Notice Jan 2010: What is an Oka manifold. Original article not referenced.
nLab page on Complex manifolds