Some helicopters do have a form of autopilot. For example, the Sikorsky MH-53E Sea Dragon has a Digital Automatic Flight Controls System (DAFCS or just AFCS). I have been told its standard in the majority of Sikorsky products, but I can't confirm this (I can for the MH-53E). The USCG HH-65 Dolphin also has AFCS. AFCS It includes such functions as Barametric Altimeter hold, Radar Altimeter hold, and a few other basic auto pilot functions. There is also an Approach/Hover Coupler that at the push of a button, the aircraft will depart, or come to a hover, and even land, all by selecting one of three buttons and manually manipulating a few knobs. It does have a few other functions but it is not CAT III capable like a B737-7XX or simular platform. It does provide, do a limited degree, hands-off flying simular to jets.
A1-H53ME-NFM-000 (MH-53E NATOPS FLIGHT MANUAL)