Supernovae of Type IIb, Ib and Ic are core-collapse supernovae whose massive progenitors have been stripped of progressively larger amounts of their hydrogen and helium envelopes. We present a selection of very well time-sampled, high-quality and homogeneous optical and near infrared (JHKS) light curves and optical spectra for a total of 20 nearby (z>0.03) SN of Types Ib and Ic, taken with the FLWO, Magellan and Gemini Telescopes. The data begin as early as two weeks before maximum light and go to late times (up to 300 days), when the supernovae are in the nebular phase. This sample doubles the world supply of well-observed stripped-envelope SN events. We discuss general properties of this population of core-collapse supernovae, including their photometric behavior. Specifically, we present data of SN 2006aj, the most recent spectroscopically-confirmed SN associated with GRB 060218, and of SN 2006jc, a supernova that shows signs of interaction with a dense He shell and dust. We see signs of aspherical explosions from nebular line profiles even in normal SN IIb, Ib and Ic. Our near infrared observations show that this band can carry a significant fraction of the bolometric flux, and is important to understand the physics of these supernovae.