It's relatively easy to manage reusability in a rocket if you don't get to orbital speeds.
The X-15 was a rocket powered spaceplane. It was launched from a B-52 jet carrier (at about 13.7km altitude) and flew to the edge of space (several flights to 80km altitude, below the FAI definition of "space", but above the USAF's definition, and two flights above FAI's 100km), but wasn't fast enough to get into orbit. Three were built and flew a total of 199 times between 1959 and 1968. This was a very successful research program, which provided a lot of data for development of the space shuttle as well as demonstrating the value of combining human pilots with automated systems.
Various other rocket-powered aircraft have flown multiple times atmospherically, for example, the Me-163 and Bell X-1, but I imagine you're primarily looking for spacecraft with this question.