From start to finish, an individual action potential lasts about 1ms, followed by a few millisecond refractory period. There is probably not much biologically-relevant activity happening at faster timescales.
However, one often wants to "sort" spikes so that those arising from individual neurons are grouped together. To do so, you need to sample fast enough to capture the shape of the action potential, not just the fact that it happened. This usually requires sampling rates in the 10s of kHz. (~30 kHz would be good).
