I closed my account without having a "full featured" alternative ready. Instead, I used the the mailbox feature provided by my domain registrar[1]. I initially set out to only use this as a temporary arrangement, but the quality of service has been so excellent that I've had no reason to move from it.
Keep in mind, because of this move, I'm no longer a "typical" email user. At least, not what has become typical of email. I use it purely as a personal communication tool. Not as an information archive, password manager, file storage or any other (mis)use of the thing that has seemed to become standard these days.
I access it through a desktop client via IMAP, but they also provide webmail access via an instance of the GPL licensed Roundcude[2], which I use extremely rarely.