The "penny test" tread depth check doesn't hold water.
Yes, U.S. coins can be substituted as a tire tread depth gauge to measure the critical, final few 32nds of an inch of remaining tread depth.
Place a penny into several tread grooves across the tire. If part of Lincoln's head is always covered by the tread, you have more than 2/32" of tread depth remaining – the minimum legal amount of tread required.
Place a quarter into several tread grooves across the tire. If part of Washington's head is always covered by the tread, you have more than 4/32" of tread depth remaining.
Tire Rack has tested the effects of tread depth on wet stopping distances. Using a BMW 325i and a Ford F-150 Supercab 4x2 with three sets of tires for each vehicle (Michelin for the BMW and BFGoodrich for the truck): ): a brand-new set, a set shaved to 4/32-inch, and a set shaved to 2/32-inch. The test track was then dampened to simulate moderate rain conditions. After repeated stops from 70 mph were conducted with both vehicles on all three sets of tires, average stopping distances were calculated.
When your tires are worn to 2/32-inch of tread depth there's not enough area for water to be evacuated by a tire, which causes an increased stopping length due to hydroplaning. In wet conditions, it's fairly clear that the more tread depth available, the easier it is for a tire to do its job.
Don't let this be you next time it rains!