Spinning should probably be turned off for any 2D (or higher) experiment. Spinning will cause a modulation of the signal as a function of the evolution time, which will result in T1 noise (big streaks in the F1 direction of the transformed data). The shim on modern instruments is usually so good that it is rarely necessary to spin 5mm samples, even for 1D.

Spinning your sample is not reccomended during 2D experiments, especially if you are using gradient-enhanced techniques. In a 2D NOE experiment, spinning the sample wil increase the rate of diffusion in your sample and some of the NOE might be lost as the molecules of interest bounce around in your sample. Remember that NOE is transferred through space and it might even affect neighbouring molecules if they collide, transferring some nuclear magnetization. You don't loose sensitivity by spinning but you don't emprove lineshape either. If you are looking for better lineshapes try shimming better and using a proton observe probe (inverse probes on Bruker spectrometers: BBI, SEI, etc). Spinning will result in a loss of NOE in your sample and your spectrum might not be useful anymore, especially if your sample is dilute.