ROSAT blank field sources.: I.: Sample selection and archival data

We have identified a population of "blank field sources" (or "blanks") among the ROSAT bright unidentified X-ray sources with faint optical counterparts. The extreme X-ray over optical flux ratio of blanks is not compatible with the main classes of X-ray emitters except for extreme BL Lacertae objects. From the analysis of ROSAT archival data we found no indication of variability, and evidence for only three sources, out of 16, needing absorption in excess of the Galactic value. We also found evidence for an extended nature for only one of the five blanks with a serendipitous HRI detection; this source (1WGA J1226.9+3332) was confirmed as a z = 0.89 cluster of galaxies. Palomar images reveal the presence of a red (O-E greater than or equal to 2) counterpart in the X-ray error circle for six blanks. The identification process brought to the discovery of another high-z cluster of galaxies, one (possibly extreme) BL Lac, two ultraluminous X-ray sources in nearby galaxies, and two apparently normal type 1 active galactic nuclei (AGNs). These AGNs, together with four more AGN-like objects, seem to form a well-defined group: they present unabsorbed X-ray spectra but red Palomar counterparts. We discuss the possible explanations for the discrepancy between the X-ray and optical data, among which are a suppressed big blue bump emission, an extreme dust-to-gas ratio (similar to40-60 times the Galactic ratio), a high-redshift (z greater than or equal to 3.5) quasar nature, an atypical dust grain size distribution, and a dusty warm absorber. These AGN-like blanks seem to be the bright ( and easier to study) analogs of the sources that are found in deep Chandra observations. Three more blanks still have an unknown nature.