In molecular crystals one can see not just small quantitative changes, such as changes in bond lengths of the order of a few hundredths of an Angstrom, but actual changes of the geometric arrangements of the molecules in the crystal. This "isotopic polymorphism" is nicely reviewed in a recent article by Klaus Merz and Anna Kupka.
A specific example is pyridine. The H and D polymorphs are shown below and taken from here. Note, the hydrogen bonds involved are relatively weak C-H...N bonds.
Why does this sensitivity to H/D matter in a broader context?
1. Understanding and calculating the relative stability of different possible crystal structures for organic molecular crystals represents a formidable theoretical challenge. This shows that one needs to have an accurate calculation of the relative zero-point energies of the competing structures, making the challenge even greater.
2. As I posted before, an intriguing and outstanding problem concerning superconducting organic charge transfer salts is how H/D substitution allows one to tune between Mott insulating and superconducting states.
3. Protons matter in molecular biology! Yet one cannot "see" them with X-ray crystallography. The alternative, which is increasing in viability and power, is neutron crystallography. However, this usually means replacing the hydrogens with deuterium. But, this means that the structure one determines is not necessarily the native structure. In many situations, the differences are probably small. However, in situations with short hydrogen bonds [see e.g. here] the difference could be significant.