Hate disturbance from the messaging app or don't want anybody to know that you are online yet you want your data connection on. All you need do is to Turn off your Whatsapp Application and continue with your browsing. Well, I am referring to Android users.

Step1: Go to Settings >Applications* > Running. (some will say "App", or "Application Manager")

Step 2: Locate WhatsApp and click on "Stop". 

Step 3: Confirm stopping the application if asked.

If you want to restart the application, simply launch it and it'll start running again.

Another option is by downloading a task killer from the Play Store, and use it to stop any application you want to stop. Both methods works for other apps.