Yes, MSMBuilder is software package that uses them explicitly in protein dynamics simulations. The rationale behind it is it allows you to take trajectories from molecular dynamics simulations, and construct a markov state model out of the conformational state space of the protein. This is extremely useful in MM simulations, because it allows for the conformational space to be sampled by many smaller trajectories, instead of one longer trajectory where it is highly unlikely to sample the full state space anyways(gets stuck in local minima). This allows for molecular dynamics simulations to be done as High Thruoughput computing instead of HPC. Its the rationale behind Folding@home.

Edited for clarification

Yes, they're all over the place and lend themselves well to nucleotide and protein sequence data. Hidden Markov Models are used in the Glimmer gene finding algorithm for example.