Sadly, there’s no way to delete your account.
All you can do, really, is remove all your personal data from it. From their FAQ (http://forum.baby-gaga.com/faq-1.html#q8):
Currently, this option is not available. If you’d like your presence on Baby Gaga to be less visible, you can go into the forums and delete all of your posts. The easiest way to stop interacting with Baby Gaga altogether is to simply turn off all your email alerts and subscriptions (go into “my account” on your member menu and de-select all your subscriptions under the “subscriptions” tab).
For more information and user tips, have a look as this thread: