A common example is the case of carbon monoxide, which has a very small dipole moment.
These have residual entropy, because the atom-by-atom microscopic structure can be arranged in a huge number of different ways across a macroscopic system.
One of the first examples of residual entropy was pointed out by Pauling to describe water ice.
The existence of these multiple configurations (choices for each H of orientation along O--O axis) that meet the rules of absolute zero (2-in 2-out for each O) amounts to randomness, or in other words, entropy.
A great deal of research has thus been undertaken into finding other systems that exhibit residual entropy.
This material is thus analogous to water ice, with the exception that the spins on the corners of the tetrahedra can point into or out of the tetrahedra, thereby producing the same 2-in, 2-out rule as in water ice, and therefore the same residual entropy.