ProtonMail, an encrypted webmail service, has apparently opened up its beta to the general public; I had signed up to try it months ago and finally got an email inviting me to set up an account.
It's a webmail service such as Gmail, Yahoo Mail, etc., but messages between ProtonMail users are automatically encrypted. The encryption is done in the browser, and ProtonMail says it does not have access to a user's encryption password. (The site requires two passwords, a login password and an encryption password.)
ProtonMail would seems to be a simple option for people who are interested in trying email encryption.
Note that probably the most secure approach is to keep control over your own keys and encryption. That can be done using Thunderbird as your email client with Enigmail as an add-on. That can also be done using Mailpile, which probably will be the best program to use once the development finishes.
The Mailpile beta has been released. It's very promising and I have been testing it, but it does still have some bugs.