Android Studio doesn't recognize my device

Did you try to configure the "Media Mode" in "Camera (PTP)" instead of "Media device (MTP)"? This is sometimes solving the issue. Its in the USB Computer Connection options of your Android device, you should see an "authorize" dialog then.

Update 04/2017: looks like it has been fixed in Android 7.1.2

I have done numerous ways of handling that issue. Finally it has worked! I am using LG Optimus II, but I believe the following steps are generic to other Android devices as well.

Step 1:

Make sure your device is enabled for development. If yes, go to Step 2, otherwise go to Settings > About phone and tap Build number seven times which is magic number :-). Now Developer Options is available in the Settings.

Step 2:

Before you plug your device to PC, Go to Settings > Developer Options and select USB Connection method.

Step 3:

Plug the phone to the PC, you are given options for the USB Connection method, and please select Internet connection. Make sure you have connected to the Internet. By the way, I have changed MTP to PTP, it did not work for me. Therefore, I tried Internet connection mode, then it worked.

Step 4:

Run the app in the Android Studio, it will ask you to authorize the device for development, and select YES!.

Step 5:

Run the application via Android Studio and choose the device, not emulator, and BINGO! Welcome to Android development board.

Try swapping the USB port the cable is plugged into.

Sounds crazy but after 20 minutes of debugging this worked for me.