Why wouldn't we?
More seriously, at the end of the initial boost a rocket is typically not high enough above the Earth's surface to enter a stable circular orbit, let alone an orbit suitable for say a telecoms satellite (which is much higher). So the initial boost puts it into an elliptical orbit with it's upper end (apogee) at the altitude of the desired final orbit. Then when it reaches that altitude, a further thrust (whether by turning the original rocket back on, or by using another one) increases its velocity until the orbit is circular.
For some applications, an elliptical orbit is actually better. For instance the Juno probe is in an elliptical orbit around Jupiter so that it can spend as little time as possible in Jupiter's radiation belts, while getting close up observations and having time to send data back to Earth. It also makes it easier to adjust the orbit to pass over different parts of Jupiter on different orbits.