In the old, pre-GPS days, airline pilots could set their course by listening in for radio navigation beacons-these transmitted a continuous wave signal, with you could use to set your compass heading.
When I was a kid, my Dad had a Grundig SW receiver-if you tuned in to one, you heard noise-it sounded like an electric drill.
Now that we have inertial navigation and GPS, is this old-fashioned system still used? If so, who maintains it?
The VOR system is still in service and not going anywhere in the near future but may eventually be replaced with GPS.
Sorta.
NDB = Non Directional Beacon + Low frequency, ( lots of static sometimes ) there is an instrument that just points to it, they broadcast a Morse code signal for positive indemnification.
Also known as an ‘outer marker’ on the ILS landing system. A few are still used around the world for navigation. US ones are maintained by the FAA.
If you are old enough to have flown back in the bad old days, like me, learning to fly instruments included using an ADF approach. Automatic Direction Finder which is just an approach that only uses an NDB as the only aid.
Also farther back before VOR even there was only low frequency radio beacons. There no instruments that would just point to them, the pilot had to use one of those little round antennas to find where the beacon was. The beacon also sent out a Morse Code signal of an A or an N which would overlap along a narrow band in 4 different directions and when they did the pilot would hear just an .- or a -. but they would combine into a continuous tone so the pilot would know he was on the thin overlap line. ( Over simplification of the system )
I still have some old sectional & WAC’s that show them.
They really did not give you a compass heading in so many words as to fly this compass course & you will get there. But if you followed the needle you would find the beacon. You might make a quarter circle doing that if there were cross winds unless you you followed the procedures in which you figured out your own compass heading.
Pretty much a lost art in the modern world now but in some out in back of no where it is still used.
http://en.wikipedia.org/wiki/Non_Directional_Beacon
http://en.wikipedia.org/wiki/Low_frequency_radio_range
All Maintained by the FAA
Evidently LORAN is still used in parts of the world, but US and Canadian systems have been discontinued:
the Decca Navigator system has been switched off here in 2000, though it continued in Japan for a little longer.
I loved the LORAN-C rollout.
LORAN was originally a maritime system, and, as such, did not cover inland areas.
Huge rush to get LORAN beacons up to “close the inter-continental gap”.
As soon as LORAN-C was up and FAA-certitied, the avionics mfg’s rolled out $10K FAA-approved receivers for aircraft.
The next year, the DoD brought up the noon-precision GPS signal (the precise signal is reserved for the military).
I wonder what those Loran units are going for these days…
Where I normally flew, I got some amazing accurate repeatable points with Loran. 
Made some poor man approaches for my emergency places. 
Those were some good units… 
They are very much still in use. VOR and DME are the most common ground based navaids. With the VOR you can find out what “radial” you are on. The radial is a bearing from the beacon. You dial in the radial you want to be on and the nav display gives you a course bar presentation showing you either left or right of the radial. When the course bar is centred you are on the radial. The radial you are is independent of your heading. DME is distance measuring equipment and does just that, tells you how far away you are from the beacon. With a VORDME or two VORs or two DMEs you can get a position fix.
In my neck of the woods (Australia) it is still a requirement to monitor ground based navaids when within the rated coverage and the airway is definied by those ground based aids, even if you are actually using GPS for your primary navigation.
Airliners don’t have GPSs per se, they have flight management computers or systems (FMC or FMS) that take inputs from GPS, VOR, and DME to arrive at a best computed position. The GPS input is heavily weighted and you will generally find that the FMS position is the same as the GPS position however the ground based aids are still monitored and if there is a discrepancy between the VOR DME position and the GPS position you will start getting error messages from the FMS. Some FMS units will give preference to a DME/DME position over anything else provided there are two DMEs in range.
A big issue with GPS is that it can’t easily tell you that it is not working properly. A ground based navaid has a morse ident and you can see if it is functioning correctly. If you have enough satellites in a GPS postion the FMS can work out if one of them is giving bad info, but if you only have enough for a basic position there is no way to know if the position is good or not without comparing it to VORs and DMEs.
Marker beacons (including outer marker, middle marker, and inner marker) aren’t NDB type navaids, they just broadcast a tone that you can only hear when you pass directly over the top, you can’t get your ADF to point at one. NDB type beacons when used as part of an ILS used to be known as “locators” but now just seem to get called NDBs. A locator outer marker is a combination of a marker beacon and an NDB.
Still in common use in Australia. A hand flown raw data NDB approach with a failed engine, down to a circling approach in minimum weather at night is still part of our 6 monthly simulator checks and there are aerodromes we fly to that are only serviced by an NDB or a GPS approach.