You can have a domain registered with Gmail or Rackspace Mail or whatever, and use the SMTP credentials they give you for outbound, while keeping MX records point to your own SMTP for inbound. Or you can let them process the inbound as well (fighting spam for you) and you just forward everything (or sweep via IMAP) and put it into your own Dovecot.
This way you control what's important to you (email storage/backups/etc) but outsource delivery and spam filtering.