Connect WordPress with Gmail without smtp

The biggest pain in setting up a wordpress site is getting it connected with an email account, to use as the sending account for system messages. This usually requires finding some obscure smtp settings from your email provider, adding credentials that will need to be updated again if you ever change your email, and various spam triggering actions that just make it all more painful than it should be.

I used Zapier recently to automate some notifcations that are sent out by email. Zapier has a Gmail connector that is as simple as logging into your gmail account inside their app, and then zapier has the access needed. No fiddling with a bunch of settings and hoping it works- it just seems to work, and pretty well.

I am looking for the equivalent of this simplicity for use with wordpress- a plugin that allows a simple connection to gmail using your gmail or google apps domain account login info, and then it just works.

This is a work in progress- I will add any solutions I find here. Please add your suggestions in the comments.