Results are presented from a uniform and systematic analysis of more than 200 X-ray observations of 36 BL Lacertae objects obtained from the EXOSAT archive. All but two objects were detected at least once. Strong luminosity variability, which reached a factor of 30 in one case, was a common property of these objects. Variability was usually more pronounced in the hard (0.7-8 keV) X-ray energy band than in soft X-rays, implying hardening of the spectrum as the sources brightened. This behavior is opposite to that observed in some Seyfert galaxies. Four objects (ON 325, 1E 1402.3 + 0416, PKS 2005-489, PKS 2155-304) showed large-amplitude flux variations on time scales of a few hours. In addition, 1H 0414 + 009, PKS 0548-322, Mrk 421, and Mrk 501 changed their intensity by ≈20%-40% on the same time scale. There were no long-term trends in the X-ray emission of any of the objects that were well monitored over a long period of time. The commonest form of variability in the soft X-ray band can be represented by small-amplitude variations about a quiescent level that remains approximately constant for years. A statistical analysis shows that, on average, BL Lacs spend less than 10% of the time in flares that involve luminosity variations of factors of 2 or more. The αox-αro diagram of the objects in the sample allows the identification of two subclasses of BL Lacs characterized by different intrinsic properties, namely, the Q-BL Lacs, which include most of the classical radio-selected objects and show energy distributions similar to those of other radio-loud active galactic nuclei, and the X-BL Lacs, which include all the optically and X-ray discovered objects. X-BL Lacs probably constitute the predominant population. There were no obvious differences in the X-ray variability properties of the two subclasses. Analysis of the soft X-ray emission reveals no evidence for intrinsic absorption in excess of a few times 1020 atoms cm-2 in any of the objects for which data of sufficiently good quality were available.