How prevalent is traditional radar tracking of commercial aircraft?
There are many surveillance technologies available to track aircraft. 

Radar is the most common technology used for ATC (Air Traffic Control) surveillance. Basically there are two varieties:


Primary radar

This type of radar sends a high energy radio pulse which reflects of the aircraft. The time delay of the received echo is a measure of the distance.
The characteristics of the transmitted radio pulse. Since aircraft don't have to participate for this radar to work this radar principle is mostly used for Air Defence purposes.

ATC primary radar usually has a maximum range of about 50-100NM, but can exceed 200NM. Primary radar is mostly used for airspace protection (monitoring unauthorized access) and airport surface control. These radars have a limited maximum range but a very low minimum range and provide reasonable accuracy.

Long range primary radar is expensive to operate. Due to the free space signal loss, long range radar needs to transmit a very powerful pulse and receive an very weak echo. The associated infrastructure (large antenna, active cooling) and power requirements make long range primary radar very expensive. 

Military use of primary radar includes over the horizion (OTH) radar which has ranges well over 1000NM. These radars are geared towards detection of incoming missiles and aircraft and not suitable for air traffic control due to their lower accuracy.   
Secondary radar

Secondary radar is the most common surveillance technology used by ATC.

This type sends a radio signal to the aircraft's transponder to which the transponder replies with its own radio signal. Again the time delay is a measure of the distance. The transponder can encode additional information about the aircraft (such as altitude or identity) in the reply. This radar technology relies on the correct functioning of the radar transponder. 

Because the radar relies on transmission of energy from the aircraft, the transmitter needs less power than a primary radar. The maximum range of secondary radars can exceed 250 NM for aircraft flying high enough (above the horizon). Not all secondary radars are operated at that range though, airport radars are often limited to 50 - 100 NM.


Radar signal horizon


Then there are a number of surveillance technologies which are a bit different than radar: 


(Wide Area) Multilateration

This technology uses multiple receivers spread over an area. By accurately comparing the times that an aircraft's transponder signal arrives at the different receivers the system can calculate where the signal must have been transmitted from. The transponder signal must be received by at least four receiver to get an accurate position. The accuracy of multilateration is best in the area surrounded by receivers; outside that area the accuracy of the system degrades quickly. A provide with enough receivers, a Wide Area Multilateration system can cover vast airspace volumes. 
ADS-B

Automatic Dependent Surveillance - Broadcast is a surveillance technology that relies on the aircraft transmitting their position twice per second. A simple antenna and receiver is all that is required to receive these positions. Since the signal comes from the radar transponder, the above signal horizon figure applies. A very sensitive receiver can detect high flying aircraft far away. Not all aircraft are yet equipped with ADS-B but most passenger transport aircraft are.

The company Aireon is equipping satellites with ADS-B, so in 2018 there will be oceanic ADS-B coverage.  
ADS-C

Automatic Dependent Surveillance - Contract is again a surveillance technology that relies on the aircraft transmitting their position. Contrary to the broadcast counterpart which transmits to all interesting parties, ADS-C addresses its transmissions to the contracted ATC facility. The data goes via a satellite link or over VHF when the aircraft is flying over land. Because of the satellite link, coverage is global (except the poles).
ADS-C reports are less frequent that radar or ADS-B reports, typically the system only reports at specific reporting points. 

ADS-C is not installed on every aircraft, mostly on intercontinental transport aircraft. It is used mainly over the Pacific and the Atlantic. 
Verbal position reporting

Not really a surveillance technology, but used in areas where there is no other means of surveillance available. The pilot reports his position over the radio to air traffic control. The maximum range of the radio transmission is the limiting factor here. Using HF radio, global coverage is achievable. The transmissions suffer a lot from static noise and sometimes other aircraft have to relay messages if no proper direct communication between ATC and the aircraft can be achieved.