You should never let members delete their accounts or their entire posts. It will make threads look confusing, especially with posts quoting said deleted members' posts.
I'm okay with account deleting, so long as it is admin approved (some sites require an admin to approve it anyway). Some systems don't delete posts when a member deletes their profile, unless specifically told to. Although mass post deletion bothers me, I respect the user's decision and if they want to have everything gone then that's what I'll do.
Personally, if a user requests to delete their account, I will grant it with good reason. Some people may do it for safety, especially if they are being stalked. However I don't just allow users to delete their account on their own.