Nathan Bransford, a literary agent at Curtis Brown, is holding his 2nd annual 1st paragraph contest, hosted on his blog.
The prizes are either a query or partial critique. Whooeee... I think this is an interesting forum for a contest. All of the posts are public, so we can see the competition, and the comments are also public. The deadline is this Thursday, finalists are to be announced on Friday, and then participants will vote on which finalist will be the grand prize winner.