The nozzle is the part of a rocket that limits the speed of the exhaust velocity. (It's also the part that converts the pressure and temperature of the expanding propellant into velocity.)
The speed of sound in the exhaust likewise regulates the expansion of the propellant gas.
For rockets using nozzles, the exhaust velocity can be expressed as
$$V=\sqrt{\frac{2 \gamma R_{{}^{\circ}} T_{{}^{\circ}}}{(\gamma -1) \mu
}\left(1-\left(\frac{P_e}{P_c}\right){}^{\frac{\gamma -1}{\gamma
}}\right)}$$
(in the form from Hash's self-answer elsewhere; k is used instead of $\gamma$ and M instead of $\mu$ in Basics of Spaceflight.)
Restrictions on the exhaust temperature $T$ are implied by the temperature that the nozzle can withstand. $\gamma$, $\mu$, and $R$ have to do with the choice of propellant. $\gamma$, $R$, and $T$ also directly relate the speed of sound in a gas.
As in Tom Spilker's answer, ion engines avoid that limitation because they don't rely on the gas's expansion to provide the exhaust velocity. The directed application of electromagnetic fields to an ionized exhaust stream allows higher velocities to be imparted.