Context. Molecular filaments have received special attention recently thanks to new observational results on their properties. In particular, our early analysis of filament properties from Herschel imaging data in three nearby molecular clouds revealed a narrow distribution of median inner widths centered at a characteristic value of about 0.1 pc. Aims. Here, we extend and complement our initial study with a detailed analysis of the filamentary structures identified with Herschel in eight nearby molecular clouds (at distances <500 pc). Our main goal is to establish statistical distributions of median properties averaged along the filament crests and to compare the results with our earlier work based on a smaller number of filaments. Aims. We use the column density (N_H2) maps derived from Herschel data and the DisPerSE algorithm to trace a network of individual filaments in each cloud. We analyze the density structure along and across the main filament axes in detail. We build synthetic maps of filamentary clouds to assess the completeness limit of our extracted filament sample and validate our measurements of the filament properties. These tests also help us to select the best choice of parameters to be used for tracing filaments with DisPerSE and fitting their radial column density profiles. Methods. Our analysis yields an extended sample of 1310 filamentary structures and a selected sample of 599 filaments with aspect ratios larger than 3 and column density contrasts larger than 0.3. We show that our selected sample of filaments is more than 95% complete for column density contrasts larger than 1, with only ~ 5% spurious detections. On average, more than 15% of the total gas mass in the clouds, and more than 80% of the dense gas mass (at N_H2 > 7 × 10²¹ cm⁻²), is found to be in the form of filaments. Analysis of the radial column density profiles of the 599 filaments in the selected sample indicates a narrow distribution of crest-averaged inner widths, with a median value of 0.10 pc and an interquartile range of 0.07 pc. In contrast, the extracted filaments span wide ranges in length, central column density, column density contrast, and mass per unit length. The characteristic filament width is well resolved by Herschel observations, and a median value of ~0.1 pc is consistently found using three distinct estimates based on (1) a direct measurement of the width at half power after background subtraction, as well as (2) Gaussian and (3) Plummer fits. The existence of a characteristic filament width is further supported by the presence of a tight correlation between mass per unit length and central column density for the observed filaments. Results. Our detailed analysis of a large filament sample confirms our earlier result that nearby molecular filaments share a common mean inner width of ~0.1 pc, with typical variations along and on either side of the filament crests of about ± 0.06 pc around the mean value. This observational result sets strong constraints on possible models for the formation and evolution of filaments in molecular clouds. It also provides important hints on the initial conditions of star formation.