Yes, bats can hear exceptionally well.

More Info: Bats not only hear well, they are the most sensitive of all mammals when it comes to distinguishing high frequencies.

How Do Bats Communicate?

Some species of bats use their keen sense of hearing to both navigate and find food in a process called echolocation.  During this process, the bat emits a high-pitched sound through its mouth or nose. This ultrasonic sound will then travel through the air until it hits and object at which time it will bounce back to the bat for interpretation.

The Anatomy of a Bat's Ear

Research has demonstrated that the bat's ears and keen sense of hearing are instrumental to echolocation.  When the tragus and pinna, the outer part of the ear, were deflected, the rate at which the bat's were able to capture prey dropped dramatically.  Once the bat sends out an ultrasonic sound, the ears help the bat interpret the identity, size, and location of the object from which the ultrasonic sound bounces. 

How Good Is Good?

A bat's hearing is more than seven times keener than a human's is on the high frequency scale. Humans can hear frequencies between 20-20,000 Hertz, 16,000 Hertz being the highest frequency that the majority of people can distinguish.  A bat on the other hand, can hear frequencies between 1,000-150,000 Hertz.  Dogs, that are generally thought to have a keen sense of hearing, don't even come close.  The highest frequency a dog can hear is double that of human's or 46,000 Hertz.