The evolution of a Type IIn supernova (SN IIn) is governed by the interaction between the SN ejecta and a hydrogen-rich circumstellar medium (CSM). SNe IIn thus allow us to probe the late-time mass-loss history of their progenitor stars. We present a sample of SNe IIn from the untargeted, magnitude-limited surveys of the Palomar Transient Factory (PTF) and its successor, the intermediate PTF (iPTF). To date, statistics on SN IIn optical light curve properties have generally been based on small ( 10 SNe) samples from targeted SN surveys. SNe IIn found and followed by the PTF/iPTF were used to select a sample of 42 events with useful constraints on the rise times as well as with available post-peak photometry. The SNe were discovered in 2009-2016 and have at least one low-resolution classification spectrum, as well as photometry from the P48 and P60 telescopes at Palomar Observatory. We study the light-curve properties of these SNe IIn using spline fits (for the peak and the declining portion) and template matching (for the rising portion). We study the peak-magnitude distribution, rise times, decline rates, colour evolution, host galaxies, and K-corrections of the SNe in our sample. We find that the typical rise times are divided into fast and slow risers as 20 ± 8 d and 50 ± 15 d, respectively. The decline rates could possibly be divided into two groups (with slopes 0.013 ± 0.008 mag d −1 and 0.040 ± 0.014 mag d −1 ), but this division has weak statistical significance. We find no significant correlation between the peak luminosity of SNe IIn and their rise times, but the more luminous SNe IIn are generally found to be more durable and the slowly rising SNe IIn are generally found to be slowly declining. The SNe in our sample were hosted by galaxies of absolute magnitude −22 Mg −13 mag. The K-corrections at light-curve peak of the SNe in our sample are found to be within 0.2 mag for the observer's frame r-band, for SNe IIn at redshifts z < 0.25. Applying K-corrections and including also ostensibly "superluminous" SNe IIn, we find that the peak magnitudes are M r peak = −19.18 ± 1.32 mag. We conclude that the occurrence of conspicuous light-curve bumps in SNe IIn, such as in iPTF13z, is limited to 1.4 +14.6 −1.0 % of the SNe IIn. We also investigate a possible subtype of SNe IIn with a fast rise to a 50 d plateau followed by a slow, linear decline. iPTF13agz, iPTF13aki, iPTF13asr, iPTF13cuf, iPTF14bcw, iPTF14bpa, iPTF15aym, iPTF15bky, iPTF15blp, iPTF15eqr, iPTF16fb. ⋆ Based in part on observations made with the Palomar Transient Factory and intermediate Palomar Transient Factory surveys.