Why is my GS3 automatically answering incoming calls. I am not using a headset/bluetooth. The phone can be in an entirely different room when a call is automatically answered.
Is your Settings > Language And Input > Voice Command for Apps 'On'? Sometimes it picks up something in the background and answers the calls.
If turning off that doesn't work, try to do a factory reset on the phone.
Unfortunately, if even that doesn't work, you will have to get it inspected at a Service Center.
Try inserting a 3.5 Headphones with mic and call your cell.
If it will answer automatically it is a software problem, try to remember what things have you changed/installed before that was happend.
If it fix the problem, take out the Headphones and try calling your cell. Sometimes the AUX 3.5 Jack isn't recognizing when a device is plugged-out (mostly because of a damaged headphones/headphone's Jack), this could be the problem.
On my T-Mobile SGH-T999 Galaxy S3 (Android 4.1.1), there is a "S Voice" icon under Apps. If you start the app and skip the setup questions, you will be prompted "What would you like to do?".
At this point press the menu button and choose Settings > Control apps, turn off "Control apps: Use voice commands to control device".
Hope that helps!