It's ridiculous how many different mobile messaging services are out there right now. Looking at my own phone I've got Blackberry Messenger, Facebook Messenger, Hangouts, Line, and WhatsApp installed, all to communicate with different people in my life. Most of these services are mobile centric, but many of them have desktop counterparts too--making life easier when you're stationed in front of your PC.
If you need to send and receive messages from your favorite mobile messenger on your PC here's a list of the more popular services that offer official desktop counterparts.
WhatsApp: The Facebook-owned messaging service introduced a web app in January. It's not an independent service, however. To use WhatsApp on the web your phone needs to have WhatsApp installed and be connected to the Internet while you're using the web app. Check it out at web.whatsapp.com.
Facebook Messenger: You've always been able to access Facebook messaging via the social network's website, but the company recently introduced a separate web app at Messenger.com. Just sign-in with your Facebook account and you're good to go.
Line: This service isn't as popular in the U.S. as it is in Asia, but Line's American user base is growing. The service offers desktop apps for Windows and Mac, as well as a modern UI app for Windows 8 and up. Line requires you to have its app installed on your phone before you can use the desktop app.
Viber: Viber has had a Windows desktop app for nearly two years and a modern UI app for almost as long. There are also apps for Mac and Linux. Like other services you'll need to have Line on your phone first before moving over to the PC.
Hangouts: Google's all-in-one messaging service is invading key parts of the company's services including Gmail, but for Chrome users there's also a separate Hangouts app. Hangouts for Chrome functions just like a desktop program complete with notifications and fires up automatically when you open Chrome.
iMessage: Windows users are out of luck, but Mac users have been able to connect iMessage to their desktop since Mac OS x 10.8.2 Mountain Lion.
Pushbullet (for Android): This isn't a messaging service but an app that puts mobile notifications on your desktop. In February, the company came out with an update that lets you respond to messages from multiple services on your PC including WhatsApp, Telegram, Hangouts, Facebook Messenger, and Line. The Hangouts implementation is a little weird, however, as it requires you to have the Android Wear app installed on your phone.
For everything else, there's AirDroid
The list above covers most of the major messaging services, but if you have an app that isn't covered or are just using a generic SMS app on an older Android device try out AirDroid. This Android-specific app lets you get mobile app notifications on your desktop. Since AirDroid 3 you've also been able to mirror rooted devices and a few officially supported devices on the desktop giving you direct access to your phone from your PC.