Whether you're looking to run a marketing campaign without revealing your identity or you simply want to find out who has been emailng, Jestit for iPhone and iPad will allow you to send emails and reply to your existing ones while remaining anonymous to the recipient.
I'm not entirely sure what I would personally use this app for but if you've landed on this page in search of an anonymous email app then I'd say it's well worth checking out because it appears to work very smoothly.
Making a rather interesting addition to the Social Networking category of the App Store is this anonymous emailing client that will allow you to send email messages to your contacts without revealing your identity.
You can also use this app to reply to the existing emails already in your inbox, and when you send any messages out you can view receipts for sent and received messages so you know your emails are being seen.
Follow Other Users
Jestit allows you to also follow other users within a social media-like timeline format, and you can set explicit permissions based on only the people you want to be able to read your emails; this is ideal for small groups of people or organizations.
As I mentioned above, I don't see much of a purpose for sending emails anonymously but if this is what you're looking to do then it's safe to say that this app will provide you with the tools you need to achieve this.