Mid-air collisions involving airliners are rare because of the FAA and ATC. Also, mid-air collisions are not and have never been the greatest contributor to airline passenger deaths (or aviations deaths in general.) And on that count, the FAA has also been a major contributor to safety, since the regulations regarding pilot and aircraft certification, as well as operational regulations (and enforcement) are really what makes airline travel safe.

Incidentally, the biggest aviation accident in history (Tenerife) still can be felt today in how the FAA trains ATC personnel and how they choose the language that is authorized for use by ATC.

Air Traffic Controllers are highly skilled professionals, although at least 3 mid-air collisions [0][1][2] involving airliners have been a direct result of limitations in the radar technology. Newer technology like SSR gives the controllers better tools to use their skills.

Practically every pilot has heard of the Tenerife disaster, and is commonly discussed in flight schools. A lot of safety changes in aviation can be tied back to previous mishaps. In Naval Aviation, the flight standards program is known as NATOPS [3] (Naval Air Training and Operating Procedures Standardization), and the phrase "The NATOPS has been written in blood" is largely because it dramatically reduced the mishap rate, and changes are often as a direct result of previous mishaps.

[0] https://en.wikipedia.org/wiki/Hughes_Airwest_Flight_706

[1] https://en.wikipedia.org/wiki/1996_Charkhi_Dadri_mid-air_col...

[2] https://en.wikipedia.org/wiki/1986_Cerritos_mid-air_collisio...

[3] https://en.wikipedia.org/wiki/NATOPS#History.2Fraison_d.27.C...