I second the recommendation of CLRS. Another good source of applied examples is the bioinformatics literature. It may be a little tough if you don't have much b

I second the recommendation of CLRS. Another good source of applied examples is the bioinformatics literature. It may be a little tough if you don't have much background in genetics, but a lot of the basic algorithms in computational biology are essentially dynamic programming algorithms that analyze strings over the alphabets of DNA or amino acids. One of my favorite books, which is a classic and (I think) is pretty approachable for the non-biologist, is Biological Sequence Analysis by Durbin, Eddy, Krogh, and Mitchison.