Relay ME is a free Android app that forwards your texts to an email address you provide. It is ad-free and simple. If you buy pro features, you can also respond back to your texts from within your email inbox.
It does require an Internet connection for forwarding texts and it uses your phone's messaging capabilities for replies. And yes, it needs your phone to be ON!
*** Before downloading ***
Take a moment to visit our wiki at http://codolutions.com/relayme/wiki.html to know how it works. Don't get disappointed by what it isn't supposed to do.
*** Before giving us a one-star review ****
Contact us. There are many other users who happily use this app. There might be something with your phone's settings or another messaging app (GO SMS for example). We will help you fix it ;-)
*** Security/Privacy ***
Unlike many other similar applications, your texts go directly to the email server and no intermediary is involved in handling them. Emails are also sent through a safe and secure SMTP connection to your email server. Relay ME never asks for any confidential information, including your password.
*** Disclaimer ***
By downloading this application, you agree to the disclaimer at http://codolutions.com/relayme.html.
Allow turning on the service on a schedule.
Include information about when the message was received.