Low-velocity impact cratering experiments were conducted in a wet sand target. With the addition of interstitial water, the sand stiffens and the yield stress sigma(y) increases by a factor of 10 and we observe a significant change in the resulting crater shape. A small water saturation (S similar to 0.02) is sufficient to inhibit the crater wall collapse, which causes the crater diameter d to decrease and the crater depth to increase, and results in the steepening of the crater wall. With a further addition of water (S similar to 0.04), the collapse is completely inhibited such that cylindrical craters form and the impactor penetration depth delta and ejecta dispersal are suppressed. However, for S > 0.7, the wet sand becomes fluidized such that both d and delta increase thereafter. Comparing the relevant stresses, we find that cylindrical craters form when the yield stress is more than about three times larger than the gravitational stress such that it can withstand collapse. Experiments with different impactor sizes D and velocities indicate that for S <= 0.02, gravity-regime scaling applies for d. However, the scaling gradually fails as S increases. In contrast, we find that delta/D can be scaled by the inertial stress normalized by the yield stress, for a wide range of S. This difference in the scaling is interpreted as arising from d being affected by whether or not the crater wall collapses, whereas delta is determined by the penetration process that occurs prior to collapse. The experimental parameter space in terms of dimensionless numbers indicates that our experiments may correspond to impact cratering in small asteroids.