A comment here Why does "no aircraft cross directly over the pole"? indicates that modern aircraft use GPS for navigational purposes, which makes perfect sense. However, do these aircraft also have backup mechanical sensors (altimiter, magnetic compass, etc.) in case GPS signals go haywire or are not available?
In light aircraft they typically do: Glass-Panel aircraft will also have traditional "steam gauge" backup instruments of some kind.
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):
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.
Basic VOR navigation equipment (and sometimes NDB or DME aswell), altimeter and magentic compas are mandatory equipment for any IFR aircraft
It's a pretty safe bet any aircraft will have them onboard.
Also, a good side story to tell is that mechanical sensors do not act as backup to GPS: in case of altitude the 'mechanical' baro-altimeter is still the primary instrument, as for navigation the radios & IRS are still used to enhance the estimated GPS position