Aims. Our current knowledge of high-mass star formation is mainly based on follow-up studies of bright sources found by IRAS, and is thus biased against its earliest phases, inconspicuous at infrared wavelengths. We therefore started searching, in an unbiased way and in the closest high-mass star-forming complexes, for the high-mass analogs of low-mass pre-stellar cores and class 0 protostars. Methods. We have made an extensive 1.2 mm continuum mosaicing study of the Cygnus X molecular cloud complex using the MAMBO cameras at the IRAM 30 m telescope. The ∼ 3 • 2 imaged areas cover all the high-column density (A V ≥ 15 mag) clouds of this nearby (∼ 1.7 kpc) cloud complex actively forming OB stars. We then compared our millimeter maps with mid-infrared images, and have made SiO(2-1) follow-up observations of the best candidate progenitors of high-mass stars. Results. Our complete study of Cygnus X with ∼ 0.09 pc resolution provides, for the first time, an unbiased census of massive young stellar objects. We discover 129 massive dense cores (FWHM size ∼ 0.1 pc, M 1.2 mm = 4 − 950 M ⊙ , volume-averaged density ∼ 10 5 cm −3 ), among which ∼ 42 are probable precursors of high-mass stars. A large fraction of the Cygnus X dense cores (2/3 of the sample) remain undetected by the MSX satellite, regardless of the mass range considered. Among the most massive (> 40 M ⊙ ) cores, infrared-quiet objects are driving powerful outflows traced by SiO emission. Our study qualifies 17 cores as good candidates for hosting massive infrared-quiet protostars, while up to 25 cores potentially host high-luminosity infrared protostars. We fail to discover in the high-mass analogs of pre-stellar dense cores (∼ 0.1 pc, > 10 4 cm −3 ) in Cygnus X, but find several massive starless clumps (∼ 0.8 pc, 7 × 10 3 cm −3 ) that might be gravitationally bound. Conclusions. Since our sample is derived from a single molecular complex and covers every embedded phase of high-mass star formation, it gives the first statistical estimates of their lifetime. In contrast to what is found for low-mass class 0 and class I phases, the infrared-quiet protostellar phase of high-mass stars may last as long as their better-known high-luminosity infrared phase. The statistical lifetimes of high-mass protostars and pre-stellar cores (∼ 3 × 10 4 yr and < 10 3 yr) in Cygnus X are one and two order(s) of magnitude smaller, respectively, than what is found in nearby, low-mass star-forming regions. We therefore propose that high-mass pre-stellar and protostellar cores are in a highly dynamic state, as expected in a molecular cloud where turbulent processes dominate.