We have frequency-analyzed 6391 variables classified earlier as fundamental-mode RR Lyrae (RR0) stars in the MACHO database on the Large Magellanic Cloud (LMC). The overwhelming majority (i.e., 96%) of these variables have been proved to be indeed RR0 stars, whereas the remaining ones have fallen into one of the following categories: single- and double-mode Cepheids, binaries, first-overtone and double-mode RR Lyrae stars, and nonclassified variables. Special attention has been paid to the properties of the amplitude- and phase-modulated RR0 stars ( the Blazhko stars). We found altogether 731 Blazhko variables showing either a doublet or an equidistant triplet pattern at the main pulsation component in their frequency spectra. This sample overwhelmingly exceeds the number of Blazhko stars known in all other systems combined. The incidence rate of the Blazhko variables among the RR0 stars in the LMC is 11.9%, which is 3 times higher than their rate among the first-overtone RR Lyrae stars. No difference is found in the average brightness between the single- mode and Blazhko variables. However, the latter ones show a somewhat lower degree of skewness in their average light curves and a concomitant lower total amplitude in their modulation-free light curves. From the frequency spectra we found that variables with larger modulation amplitudes at the higher frequency side of the main pulsation component are 3 times more common than the ones showing the opposite amplitude pattern. A search for a modulation component with the Blazhko period in the average brightness of the individual variables showed the existence of such a modulation with an overall amplitude of approximate to 0.006 mag. On the other hand, a similar search for quadruple modulation patterns around the main pulsation component has failed to clearly detect such components at the approximate to 0.004 mag level. This means that the amplitudes of the quadruple components ( if they exist) should be, on average, at least 10 times smaller than those of the triplet components. This finding and the existence of Blazhko variables with highly asymmetric modulation amplitudes not only question the validity of the magnetic oblique rotator model but also put stringent constraints on models based on mode-coupling theories.