Not sure if I'm a typical user here

But when I get mails like this from JCrew (or the recent NetFlix issue), it almost immediately increases my trust of the company - any company that's willing to come out and so broadly say "we made a mistake" is a company I am more likely to give my business to in the future.

I've categorized this post under "User Experience" because the UX doesn't end with the UI. Apologizing for when we mess up should just be a part of the user experience. Having great error messages is a part of the user experience. Making it simple and easy to get an answer to your question from the community or technical support is a part of the user experience. etc etc...