The CFM56 is possibly the most flexible mid-size turbofan engine commercial aviation currently available. The CFM56 can be found on both the A320 family and the 737 Classic and NG families. It has also been used on the DC-8, KC-135 (707) tanker, and on the A340-200 and -300. The following tables illustrate the variations of the CFM-56 and its evolution over the years, showing the inventory of active aircraft at the end of the first quarter 2013.
The data show the number of in-service aircraft – so to compute the engine population, multiply by 2 or 4 appropriately based on aircraft type. Boeing has 33 variations of the CFM56 engine on 737 models while Airbus has 23 variants on A320 and A340 models, with several version, after continuing improvements, being used for each aircraft type. Although CFM is essentially a one engine company (until LEAP starts flying), it shares technology from its joint venture partners, SNECMA and GE. 
CFM has had a great run with the CFM56. It will be hard to replace a program that has flown on more than 9,200 aircraft. The LEAP is off to a good start, with 801 of the 1,580 A320neo family that have seen engine selections (812 remain undecided) and 1,567 Boeing 737MAX. If a similar record can be shown 30 years from now, CFM will be very happy.
The ubiquitous CFM-56 reminds me of the JT8D, which was also on a variety of aircraft in the 60’s and 70’s. But the CFM-56 essentially killed the JT8D, which P&W had taken for granted and failed to recognize that a lighter engine with a higher by-pass ratio was urgently needed. Now the table has turned again and P&W has made a comeback with the GTF. The only difference is that the CFM-56, and its replacement the LEAP, will take longer to die than the JT8D did because it is the sole engine offered on the still very successful 737 MAX. But its days are counted nevertheless. In recent years Mitsubishi, Bombardier, Airbus, Irkut and Embraer have all selected the GTF. Only Boeing did not, and that was because it could not do so for lack of adequate ground clearance on the existing 737 wing. If Boeing had elected to design a new wing for the MAX the score would be 100% for the GTF and 0% for the LEAP. And that would have been exactly what happened to the JT8D when the CFM56 came out.