Dynare comes with a database of example .mod files, which are designed to show a broad range of Dynare features, and are taken from academic papers for most of them. You should have these files in the examples subdirectory of your distribution.
Here is a short list of the examples included. For a more complete description, please refer to the comments inside the files themselves.
ramst.modAn elementary real business cycle (RBC) model, simulated in a deterministic setup.
example1.mod, example2.modTwo examples of a small RBC model in a stochastic setup, presented in Collard (2001) (see the file guide.pdf which comes with Dynare).
fs2000.modA cash in advance model, estimated by Schorfheide (2000).
bkk.modMulti-country RBC model with time to build, presented in Backus, Kehoe and Kydland (1992).