Relay ME is a free Android app that forwards your incoming texts to an email address you provide. It is ad-free and easy to set up. All you need is an email address (anywhere) and a GMail account (why? continue reading).
Please note that it doesn't backup/copy your texts, it works on new messages as they arrive and doesn't deal with the old texts. 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!
If you upgrade, you can also respond back to your texts from within your email inbox. Don't worry if you don't, all the free features will continue to work.
*** 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 leaving a poor 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 ;-)
*** Why a GMail account? ****
By providing a "free" GMail account, you help to keep this app free without being bothered by ads. Read more here: https://bitbucket.org/codolutions/relay-me/wiki/Frequently%20Asked%20Questions.md#!why-do-i-need-a-gmail-account
*** 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.
Notify the user about missed calls and multimedia messages
Allow exposing unique ID to allow troubleshooting on server side
Allow changing reply sources, supporting cases where users forward emails further to others or use + to filter emails in their mailbox.
Detect if no SMS is received and offer help
Allow 3 tries before requiring an upgrade
Minor fixes in sending replies
Fixed errors connecting to GMail