Recent high-resolution spectroscopy observations of directly-imaged exoplanets have shed light on planetary rotation rates. Similar to the Solar System gas giants, these planetary-mass objects are found to rotate well below their breakup velocities. Motivated by the observations, we explore the terminal rotation rate of gas giant planets in the unmagnetized limit. If the planet is unmagnetized and initially slowly rotating, it will accrete gas via a radially narrow boundary layer and rapidly spin up. Radial broadening of the boundary layer as the planet spins up reduces the specific angular momentum of accreted gas, allowing the planet to find a terminal rotation rate short of the breakup rate. We use our axisymmetric viscous hydrodynamic simulations to quantify the terminal rotation rate of planets accreting from their circumplanetary disks. In the talk, I will present the critical spin rates of gas giants under different disk conditions. I will show the meridional circulation flows observed in the disk outside the boundary layer, and discuss its implication on early-stage satellite formation. Lastly, I will discuss how exoplanetary rotation measurements, when combined with spectroscopic and variability studies of protoplanets with circumplanetary disks, could determine the role of magnetic and non-magnetic processes in setting planet spins.