On 10 May 1962, a Navy Sparrow III launched from a Navy Phantom jet successfully intercepted head-on another Navy missile, a Regulus II, while both were at supersonic speeds in the test range of the Naval Air Missile Center at Point Mugu, California. The Regulus had originally been the Navy's first nuclear missile deployed on submarines, but it required the submarine to surface and fuel/align the missile before firing (making it extremely vulnerable to attack) . After Regulus' replacement by Polaris, it was re-engineered as a target drone for the Navy. The Sparrow missile was developed as a radar guided missile to attack aircraft and the Sparrow III would be the first missile to allow BVR (beyond visual range) targeting.
Here's a look at the first tests of Sparrow missiles against a bomber (B-17) target in the 1950's...
Watch this 1950's news reel on the Regulus missile...