Legends: Just short of the speed of light
From The Complete Star Wars Encyclopedia (2008):
Travel between star systems was made possible by moving through this alternate universe—not all that different from realspace—in which superluminal velocities were easily reached. In ancient times, this had been thought impossible, since the legendary Drall scientist Tiran had proven conclusively 35 millennia before the Galactic Civil War that time and space were inseparable, and that the speed of light was an absolute boundary that could not be crossed. But Tiran's Theory of Universal Reference did not prohibit anything moving faster than light; it only disallowed traveling at the speed of light. If the "lightspeed barrier" could somehow be bypassed, one could theoretically shift easily from realspace to hyperspace and back.
(Source: The Complete Star Wars Encyclopedia (2008), Vol II (H-O), page 70, entry "hyperspace")
The entry goes on to explain that the hyperdrive was what first allowed this theoretical speed limit to be exceeded.