We report on the linear polarimetric observations in the Johnson I-band filter of 44 ultracool dwarfs with spectral types between M6 and L7.5, corresponding to effective temperatures in the range 2800-1400 K, and one M4.5-type star. Based on our measurements of polarization (P) and their associated error bars (σP), 11 (10 L and 1 M) dwarfs appear to have significant linear polarization (P/σP>=3). For these, the polarization degrees we have measured are in the interval P=0.2%-2.5%. Because of the typical average uncertainty of our data, we can easily confirm polarization of ultracool dwarfs that show degree of linear polarization greater than 0.4%. We have compared the two populations in our sample, the M and L type dwarfs, and have found evidence for a larger frequency of high I-band polarization in the coolest objects, supporting the presence of significant amounts of dust in L-type atmospheres. The probable mechanism polarizing the far-red optical photons of ultracool dwarfs is related to the presence of heterogeneous dust clouds nonuniformly distributed across the visible photospheres and the asymmetric shape of the objects (rapid rotations impose deviations from sphericity). In some young ultracool dwarfs, surrounding dusty disks (or shells) may also yield polarization. For polarimetric detections, a trend for slightly larger polarization from L0 to L6.5 may be present in our data, suggesting changes in the distribution of the grain properties and in the vertical height of the cloud layer. Faster rotations and important differences in metallicity and age within our sample could also account for this trend. One of the targets is the peculiar brown dwarf 2MASS J22443167+2043433 (L6.5), for which we have determined the largest I-band polarization degree in our study. We discuss that the origin of such large polarization may lie in a surrounding dusty disk (or shell) and/or rather large photospheric dust grains. Two of the likely polarized dwarfs (CFHT-BD-Tau 4, a very young, M7-type brown dwarf of the Taurus star-forming region, and 2MASS J00361617+1821104, an L3.5 field dwarf) were also observed in the Johnson R-band filter, allowing us to discuss qualitatively the size of the grains responsible for the polarization. Our data support the presence of a circum(sub)stellar disk around the young accreting brown dwarf CFHT-BD-Tau 4. The higher degree of polarization in the R band than in the I band indicates that the grain growth lies in the submicron regime in the visible photosphere of 2MASS J00361617+1821104 (effective temperature of about 1900 K). Our polarimetric data does not obviously correlate with activity (Hα and radio emission) or projected rotational velocity. Three polarized early- to mid-L dwarfs have been photometrically monitored in the I band, displaying light curves with amplitudes below 10 mmag.