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We present results of a broadband photometric study of the optical variability of six narrow-line Seyfert 1 (NLS1) galaxies observed at 172 epochs. We searched for microvariability on 33 nights. Strong evidence for microvariability was found only for our lowest luminosity object, NGC 4051, on one night. Weaker evidence suggests such variability on a few other nights for two other objects, but the data are not as convincing. Intranight variability in NLS1's is thus concluded to be rare and of low amplitude. We give illustrations of how variable image quality can produce spurious variability. We find that for well-studied non-NLS1's there is a spread in the amplitude of seasonal variability (i.e., in some years an active galactic nucleus [AGN] is more variable than in others). We find that the means of the variability amplitudes of non-NLS1's over several seasons vary from object to object (i.e., some AGNs are, on average, more variable than others). NLS1's also show a spread in seasonal variabilities. The best-studied NLS1, Ark 564, shows a range of amplitudes of variability from season to season that is comparable to the range found in broad-line Seyfert 1 galaxies (BLS1's), and in one season Ark 564 was as variable as the most variable non-NLS1. The seasonal amplitudes of variability for NLS1's are mostly in the lower half of the range of non-BLS1 seasonal amplitudes, but the absence of a suitable control sample makes a precise comparison difficult. However, on long timescales (weeks to years) NLS1's as a class are not more variable than non-NLS1's. The extreme variability seen in the X-rays was not seen in the optical. This has consequences for the models of AGNs in general as well as NLS1's in particular.