I've been using Runbox.com for two mailboxes for... many years. Their web interface is pretty great and they support just about any local mailbox solution from

I've been using Runbox.com for two mailboxes for... many years. Their web interface is pretty great and they support just about any local mailbox solution from iPhone/Android mail apps to Mailbird to Outlook, etc. Very inexpensive. They are run out of Norway and follow strict privacy standards.