  We map out the critical velocity in the crossover from Bose-Einstein
condensation (BEC) to Bardeen-Cooper-Schrieffer superfluidity with ultracold
$^{6}$Li gases. A small attractive potential is dragged along lines of constant
column density. The rate of the induced heating increases steeply above a
critical velocity $v_c$. In the same samples, we measure the speed of sound
$v_s$ by exciting density waves and compare the results to the measured values
of $v_c$. We perform numerical simulations in the BEC regime and find very good
agreement, validating the approach. In the strongly correlated regime, where
theoretical predictions only exist for the speed of sound, our measurements of
$v_c$ provide a testing ground for theoretical approaches.
