Do helicopters have an auto hover system?
Yes, advanced flight directors and autopilots for helicopters can control the aircraft in all axes, and often they have modes for hovering built in, including maintain altitude, lateral veloctiy hold, hover, and/or autolevel. 

Hovering is difficult because it requires more complex controls than maintaining altitude in an airplane.  Helicopters have a different set of control axes than fixed-wing aircraft.  Fixed wing aircraft are controlled in pitch, roll, and yaw, with thrust as an extra variable.  On a helicopter the flight path is controlled through cyclic (roll and pitch), collective, and throttle, with the anti-torque pedals as well to control yaw.  Hovering the aircraft requires controlling of the cyclic to keep the aircraft over its target with no lateral movement, and collective and throttle to maintain constant altitude, although the exact procedures are a little more complex. 

While not present on low-end helicopters due to a combination of complexity and lack of necessity, advanced autopilots for helicopters do exist.  Like on other aircraft, there is a wide variety in autopilots between simple functions to maintain attitude (often called one or two-cue guidance depending on the number of axes used) to complex FMS-integrated three-axis modes (which would be "three-cue" guidance). The FAA Helicopter Flying Handbook states, for example, that  "The most advanced autopilots can fly an instrument approach to a hover without
any additional pilot input once the initial functions have
been selected."  

On the Agusta AW139 helicopter that I'm familiar with (although I'm not a pilot), they have several modes that provide this functionality:  


an altitude mode to maintain a given altitude 
an altitude acquire mode to smoothly reach a desired altitude
an autolevel mode to level off at the end of an approach segment
a lateral velocity hold mode to maintain slow lateral motion or no lateral motion
more exotic search and rescue modes providing capabilites to transition to a hover, mark-on-target descents to predefined altitutdes, etc.


A traditional hover would be achieved by combining a low lateral velocity mode with a zero vertical speed mode like altitude or autolevel.