This happened with my daughter starting at around 8/9 months old. And again w/ my son around 12 mos old.
Turns out what they wanted was to be OUT of diapers (I can understand that - they're not exactly fun to wear!!!). We were willing to try some different things, including early and very gradual potty learning, and that worked out best for all of us, suprisingly. :)
Here's kind of what we did:
http://www.viviente.com/2005/10/how_to_do_parttime_pottyt...
Did I mention our approach was VERY gradual, responsive/team approach, and NOT rushing our kids in any way? They really preferred to NOT wear diapers and let us know in no uncertain terms (by screaming their heads of as if we were torturing them when we did try to diaper them). The truth is that we're going to need to teach them how to use the potty eventually, and ours were SO insistent/hating diapers, that it really was quite a pleasant experience... especially because all of the protesting and screaming over the diapers stopped. :)
Some resources that describe this better than I can:
* Early Start Potty Training (by Linda Sonna)
http://www.drsonna.org/ptresources.htm
* Diaper Free Before 3 (by pediatrician & mom, Jill M. Lekovic, M.D.) http://www.diaperfreebefore3.com/