The NOTS team were also involved in the Air Force's Pioneer lunar probe, which had a similar design to their own satellite and included a Thiokol lunar orbit insertion motor in place of the NOTS kick motor. In that same hectic summer of 1958 this first American moon probe attempt met a fiery end over Cape Canaveral. Its Thor Able launch vehicle carried the the first Allegany Ballistics Lab (ABL) X-248 fiberglass-cased solid motor, soon known as Altair. Altair was the first of several solid motors to be used as `universal' final stages serving a variety of launch vehicles. A prototype version of Altair, the X-241, was also used as the third stage of the NOTS vehicle. In 1959 the X-248 was used on Atlas Able and on the final Vanguard launch, while in 1960 it became the final stage for both the new Thor Delta and the all-solid-propellant Scout. Altair was also used as a final stage for the suborbital Javelin and for the Sergeant-based Journeyman and Shotput sounding rockets, and the Martin Bold Orion antisatellite weapon. A scaled up Altair, called Antares, provided another Scout stage. An improved Altair 2 version was introduced in 1963. Altair 2 was used on Scout and Delta, as well as on the unusual OV1 vehicle. Multiple OV1s were strapped to Atlas rockets and fired separately into orbit carrying their payloads.
Altair was so successful that clones of it appeared. First on the scene was Grand Central Rocket, which had now become Lockheed Propulsion Co. Its high mass ratio MG-18 stage was used instead of the X-248 on six Scout and Thor launches used to orbit classified weather satellites.
In 1965 Altair began to be phased out by another clone called the FW4, made by UTC of San Jose. The fiberglass cased FW4 was externally a slot-in replacement for ABL's Altair, and a lot of reference books fail to make the distinction between them. However, FW4 was more powerful and had the highest mass fraction of any contemporary stage. FW4 became the standard Scout and Delta third stage and was also used on the later OV1 and Burner 1 missions. It last flew on a 1983 Scout mission, being phased out in its turn by Thiokol's Star 20, also known as Altair III.
Another widely used motor is Thiokol's Star 37, which well illustrates the diverse uses that a single motor design may be put to. The first Star 37 was developed as the soft-landing retromotor for the Surveyor lunar probes in the 1960s. Shortly afterwards, it was drafted for use as the upper stage on the Thor Burner 2 rocket used to launch military weather satellites, before reaching its most well known role as the Delta rocket's final stage for most of the 1970s, replacing the Altair series in that role. The Star 37 was also used as a kick stage to boost the Pioneer and Voyager probes on their way to the outer planets, and the Helios probes down toward the Sun, the only times the Atlas Centaur and Titan Centaur probes have used an extra stage beyond the Centaur. Star 37 was also used as a payload orbit insertion motor with Atlas and Thor: the launch vehicle inserted the payload on a suborbital trajectory, and the Star 37, which is counted as part of the payload, fires at apogee to place Tiros-N class weather satellites or other payloads in their final orbits. Most recently, as launch vehicle power has increased, the Star 37 has been used as an apogee motor for the GPS navigation satellites, continuing 30 years of growth for the same basic design.
Another interesting motor from the early years is the BE-3, also known as Alcyone (one of the Pleiades). Hercules built the BE-3 as the retro-rocket for the early Ranger moon probes. The 1962 Block II Rangers were meant to dump a balsa-wood capsule on the lunar surface, and the BE-3 would fire just before touchdown to lessen the impact. In the event BE-3 never got the chance to prove its mettle, as none of the three Block II Rangers launched reached the Moon in working order. Nevertheless, BE-3 went on to be a small success story. It was used in 1963 as the kick motor for the US Air Force's Vela satellites. The Velas were placed in orbits with apogees of 100000 km, and BE-3 fired to make them circular. In contrast to Ranger, Vela was highly successful and in the late 1970s later Vela satellites were still being used to search for illegal nuclear explosions. Next, in 1964, BE-3 was used as a reentry stage for the Athena test vehicle. Athena was a small rocket launched from Green River in Utah; during descent towards White Sands the BE-3 would ignite to punch the reentry vehicle back down to the desert at high speed, simulating reentry of a larger missile. A couple years later, it was pressed into service in the same role for the SPARTA rocket, flown in Australia by a joint US/British/Aussie team and using the venerable Redstone as its first stage. For the last SPARTA flight, the profile was changed as BE-3 was fired during ascent to place itself and Australia's first satellite into orbit. In 1974, BE-3 was again used as an upper stage, this time as the fifth stage of Scout E, which flew a single mission to place the University of Iowa's Hawkeye satellite in elliptical orbit. The last use of BE-3 that I know about was in 1984, when it was again used as an apogee motor on a multiple Delta Explorer payload, and placed Germany's Ion Release Module satellite in its final orbit.
I emphasize these varied histories because there's a lot of discussion about launch vehicle reliability these days - and I think you have to factor in individual stage reliabilities. Of course the same motor flying as a launch vehicle stage and as a reentry test vehicle may have very different avionics attached to it, and we've seen in recent years commercial launch vehicles based on existing motors which have run into unexpected problems, but having burned the same motor design a large number of times has to count for something.