Recs.
Updated
Pushbullet allows you to receive and respond to text messages and other notification from you cell phone on other devices, or even the web.
SpecsUpdate
Pros
Pro Chrome notifications act as a notification drawer
Pushbullet uses Chrome notifications to act as a running list of past notification that have not yet been dismissed. This is especially useful if you receive a lot of notifications or you are not at your computer when they are received.
Pro Uses a Chrome extension for PC/Mac or a Windows application
Pushbullet is designed to use its Chrome extension although a Windows application can be used as well. The Chrome extension provides the best experience because any computer with a signed in Chrome browser will provide your Android notifications.
Cons
Con No OS X or Safari support for the foreseeable future
PushBullet will no longer support Mac OS X desktop or Safari extensions due to the "fairly annoying" approval process and other limitations. There are currently no plans to resurrect either one (source: PB developer comments on reddit.com/r/PushBullet). There ARE, however, open source apps for both available on PB's website.
Recommendations
Comments
Flagged Pros + Cons
Con Limited SMS app support
Pushbullet's support for SMS apps is very limited. It doesn't even support Hangouts, the default SMS app since Android 4.4 no to mention rare third-party apps.
Out of Date Pros + Cons
Con Can only reply to messages and for a very limited time
Pushbullet's SMS functionality is only an extension to the notification system, it is not designed to be an app to be used primarily for SMS communications. There's no way to initiate conversation, it only allows responding to them and only in if the choice to answer is made within the limited timeframe of when the notification pops up.
Con Mac users must use their browser
There is currently no desktop application for Mac users available. The Pushbullet website claims a native OSX client is "coming soon".