Inspired by the discovery of the red nova V1309 Sco (Nova Scorpii 2008) and the fact that its progenitor was a binary system with a rapidly decreasing orbital period, we have searched for period changes in OGLE binary stars. We have selected a sample of 22 462 short-period (P_orb < 4d) eclipsing binary stars observed toward the Galactic bulge by the OGLE-III survey in years 2001-2009. This dataset was extended with photometry from OGLE-II (1997-2000) and the first six years of OGLE-IV (2010-2015). For some stars, the data were supplemented with OGLE-I photometry (1992-1995). After close inspection of the whole sample we have found 56 systems with realistic period decrease and 52 systems with realistic period increase. We have also recognized 35 systems with cyclic period variations. The highest negative period change rate of -1.943 x10^-4 d/y has been detected in detached eclipsing binary OGLE-BLG-ECL-139622 with P_orb = 2.817 d, while all other found systems are contact binaries with orbital periods mostly shorter than 1.0 d. For 22 our systems with decreasing orbital period the absolute rate is higher than the value reported recently for eclipsing binary KIC 9832227. Interestingly, there is an excess of systems with high negative period change rate over systems with positive rate. We cannot exclude the possibility that some of the contact binaries with relatively long orbital period and high negative period change rate will merge in the future. However, our results rather point to the presence of tertiary companions in the observed systems and/or spot activity on the surface of the binary components.