We present measurements of the local core-collapse supernova (CCSN) rate using SN discoveries from the Palomar Transient Factory (PTF). We use a Monte Carlo simulation of hundreds of millions of SN light-curve realizations coupled with the detailed PTF survey detection efficiencies to forward model the SN rates in PTF. Using a sample of 86 CCSNe, including 26 stripped-envelope SNe (SESNe), we show that the overall CCSN volumetric rate is r(nu)(CC) = 9.10(-1.27)(+1.56) x 10(-5) SNe yr(-1) Mpc(-3) h(70)(3) at <z > = 0.028, and the SESN volumetric rate is r(v)(SE) = 2.41(-0.64)(+0.81) x 10(-5) SNe yr(-1) Mpc(-3) h(70)(3). We further measure a volumetric rate for hydrogen-free superluminous SNe (SLSNe-I) using eight events at z