Google mail. Can't kill old habits >_< And it's the only service which works on all my devices.
Posteo a German based secure provider for Mail, Calendar, Contacts and Notes. Syncing has some issues ATM.
Yahoo mail. My ever first own email (1997) - Don't use it for serious stuff since Gmail.
MailDrop Using it for things like email-to-download. Best service ever!
Edit: Lol I can't read today. 'what do you like about their APIs?'
Well, in that case, I should delete my comment and replace it by https://www.nylas.com/ It supports REST and Webhooks. The API is clean and straightforward -> docs