NMR lets you identify molecules, organic or inorganic, and do a host of interesting kinetics stuff as well. You can figure out not only how a molecule is laid out, but also how it interacts with others in a solution. Then when you get into biomolecules like peptides and proteins you can figure out conformation and such. Since those molecules are so big and so complicated your spectra can get pretty messy.

One of my favorites was when I set up a reaction in a sample tube and tracked it over time using an NMR. I discovered that a side reaction was generating something that reacted with the product I was trying to make and consuming it as the reaction went on.