Currently, it is generally believed that half of the fundamental mode RR Lyrae stars exhibit modulations of this light curves known as the Blazhko effect. The Blazhko effect produces additional equidistant peaks in the vicinity of the basic pulsation frequency components in frequency spectra. We looked for such patterns among fundamental mode RR Lyrae stars in the Galactic bulge. We found that in a total sample of 8 282 RRab stars 40.3 % of the stars exhibit the Blazhko effect. The number of Blazhko stars we identified is 3341, which is the largest sample ever studied implying the most relevant statistical results currently available. Blazhko stars with modulation occur preferentially among RR Lyrae stars with shorter pulsation periods in the Galactic bulge. Fourier amplitude and phase coefficients based on the mean light curves appear to be substantially lower for Blazhko stars than for stars with an unmodulated light curve. In addition, we discovered a new group of double-periodic stars in the OGLE Galactic bulge photometry. In 38 stars identified as fundamental mode RR Lyrae and 4 classified as the first-overtone RR Lyrae, we detected additional shorter periodicity. At this point, we cannot explain the nature of the additional periodicity.