There is a JSON API for use by mobile applications at http://app.imdb.com
However, the warning is fairly severe:
For use only by clients authorized in writing by IMDb.
Authors and users of unauthorized clients accept full legal exposure/liability for their actions.
I presume this is for those developers that pay for the licence to access the data via their API.
EDIT: Just for kicks, I wrote a client library to attempt to read the data from the API, you can find it here: api-imdb
Obviously, you should pay attention to the warning, and really, use something like TheMovieDB as a better and more open database.
Then you can use this Java API wrapper (that I wrote): api-themoviedb