I encountered this issue one Saturday afternoon, on which I happened to be working. Being a Saturday, I expected a relatively quiet day at the office. This was why, I was initially surprised when our monitoring software reported that there were more than 3500 mails present in one of our servers (say, vm.domain.com) mail queue. Within half an hour, the count had increased to approximately 5000 mails. There goes my quiet Saturday. Sigh.
Before proceeding, I would like to point out that all our servers run on CentOS and use Postfix.