Do modern aircraft still have mechanical sensors as backup to GPS?
In light aircraft they typically do: Glass-Panel aircraft will also have traditional "steam gauge" backup instruments of some kind.  


Note the airspeed indicator, attitude indicator, and altimeter to the left of the pilot's PFD.

This is however no longer guaranteed: A completely independent electronic backup system with its own power source may be used in place of the traditional "steam gauges".
This can be seen on new Cirrus aircraft, which have digital standby instruments (in the green box):


Similarly transport category jets may have traditional backup instruments:


Or they may have an electronic backup system:


Note that the electronic instruments in these cases aren't GPS-referenced: They are gyroscopic instruments with pitot and static input for airspeed and altitude/vertical speed calculation.