MightyText has been in beta for awhile, but now it's made its way to a full release. By installing the app in the Play Store and an extension for the browser of your choosing, you can view SMS/MMS messages that are sent to your phone as well as send messages through your phone via the web browser. It all works online, so there's no need to plug your phone into your computer or connect via a local network(like with AirDroid). That's nice because you'll be able to access and send texts even if you forget your phone somewhere.
Personally, I think this is great. If you're in an environment (work, school, etc.) where you really can't pull out your phone to read/send text messages, but you can be on a computer, you're able to read and send instantly. I can see myself using this a lot during long meetings. It's also nice for those times you accidentally forget your phone at home or leave it in the car. So far, it's been working flawlessly for me, with notifications coming through on my computer a split second before they pop up on my phone.