It seems like there were a number in the 70's and 80's but I haven't heard of one happening in the last ten years or so.
Some states have provisions in their constitution that provide for periodic referendums on holding a state constitutional convention. In 2010, Iowa and Michigan voters both turned down conventions by about a 1:2 margin. In Michigan, there was polling in the spring that indicated a favorable vote, and Governor Granholm was reported to be in favor.
This has a list of some more recent successful conventions:
http://www.repaircalifornia.org/about_california_other_states.php