As for planes, can they do GLONASS?
Also, the general analysis after KAL007 was that GPS should be made publicly available specifically to aid civilian navigation. They even identify what we call RAIM today to make it suitable for eventual usage as a primary navigation system.
No US military system relies on GPS for navigation. Military navigation systems use GPS as an untrusted source for fine-tuning inertial navigation within tight error bounds. Against US military systems, successfully spoofing GPS might buy you several meters of deviation. This only affects the cheapest US guidance systems, since most weapons have active terminal guidance. It is worth noting that GPS corrections are being phased out in US weapon systems, purportedly due to improvements in INS tech that moot the value of GPS corrections.
The tl;dr: GPS was developed to build a precise model of the world in peacetime that could be fed to inertial targeting and navigation systems in the complete absence of GPS. In that, it has been a massive success. US military systems have never relied on GPS for anything important. Contrary to popular media, the US has never produced GPS-guided weapons, even the cheapest systems are INS at their core.
Civilian systems use GPS for navigation, against its design, because they can mostly ignore its trivial susceptibility to hostile actors.
RNAV (or aRea Navigation) based on VOR-DME has been a thing since (at least) the 1970's. You put in a waypoint based on a radial and distance from a navaid, and then the box in the cockpit would Do Math so you could follow a track to/from that virtual navaid.
Bendix even made a cute little box for small airplanes in the 1980's that allowed you to pre-store up to 4 (or 10) such waypoint-frequency tuples and cycle through them to approximate a straight path from your origin to destination, using navaids near (but not on) your route. Given the service volume of a typical VORs, the 10 waypoints could enable a flight segment of over 2,000 km before you needed to enter more waypoints.
Around the same time, the flight management systems in airliners began to have navaid databases, allowing you derive lat/lng from the angle and distance. They could even auto-select the best local navaid to use. That enabled DME-DME area navigation, which has ~10x better precision than VOR-DME.
The flight management systems in modern airlines of course still have these databases and support navigation by ground-based navaid.
Russia still operates their version of LORAN (Chayka), too, so that's another option. By the 1980's, LORAN receivers were pretty well automated and directly produced lat/lng outputs. LORAN has worse accuracy than GPS, about ~400 meters, but is still good enough to get you to the airport.
And, as several other people have mentioned, virtually all airliners continue to carry an INS.
About a year ago I noticed that shortly after crossing Russias border the GPS stopped working. Initially I thought it was a glitch, but after a few flights it became obvious that something was going on, probably the signal was baing jammed.
Interesting that close to landing when the altitude is lower than 200m, the signal is restored.
It's unclear to me how the plane is navigating though if the GPS is jammed. Very weird...