Magnetic fields are proposed to play an important role in the formation and support of self-gravitating clouds and the formation and evolution of protostars in such clouds. We use R-band linear polarimetry collected for about 12000 stars in 46 fields with lines of sight toward the Pipe nebula to investigate the properties of the polarization across this dark cloud complex. Mean polarization vectors show that the magnetic field is locally perpendicular to the large filamentary structure of the Pipe nebula (the `stem'), indicating that the global collapse may have been driven by ambipolar diffusion. The polarization properties clearly change along the Pipe nebula. The northwestern end of the nebula (B59 region) is found to have a low degree of polarization and high dispersion in polarization position angle, while at the other extreme of the cloud (the `bowl') we found mean degrees of polarization as high as $\approx$15\% and a low dispersion in polarization position angle. The plane of the sky magnetic field strength was estimated to vary from about 17 $\mu$G in the B59 region to about 65 $\mu$G in the bowl. We propose that three distinct regions exist, which may be related to different evolutionary states of the cloud; this idea is supported by both the polarization properties across the Pipe and the estimated mass-to-flux ratio that varies between approximately super-critical toward the B59 region and sub-critical inside the bowl. The three regions that we identify are: the B59 region, which is currently forming stars; the stem, which appears to be at an earlier stage of star formation where material has been through a collapsing phase but not yet given birth to stars; and the bowl, which represents the earliest stage of the cloud in which the collapsing phase and cloud fragmentation has already started.