A Samsung phone that vibrates or even rings constantly has probably suffered some form of water damage. This is not the only possibility, but it is the most likely. The circuitry is extremely sensitive to moisture and can cause any number of problems, including constant vibration. The phone doesn't even have to come in direct contact with water to cause this kind of reaction; steam from a hot shower, for example, is enough to trigger a malfunction.
Remove the battery cover and look for a tiny, white circle. It is usually under the battery, and you should also see one directly on the battery. If both circles are snow white without a hint of pink or red, the phone does not have water damage. If they are any color but white, return the phone to Samsung for repair.
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Hold down the power button to restart the phone. Tap "Turn Off" and then power it back on, or hold down "Volume Up" and "Power" simultaneously to do a quick restart. The vibration could be a temporary issue with the operating system that will resolve itself after the reset.
Tap "Market", "Menu," and then "My Apps" to see what was installed recently. Press "Uninstall" to remove applications that were installed the same day the vibrating began. Restart the phone, and then add them back one at a time to see if the problem returns. If it does, and it's related to a new app, the developer's website may have a fix.
Clean the volume buttons, paying particular attention to the "Down" button. Some cellphones vibrate when the down button is depressed. It continues to vibrate until you let go, which indicates your button might be stuck. Apply a small amount of detergent to a cloth, or use a cleaning solution provided by Samsung for the best results.
Update the firmware if the problem persists. If the vibrating problem is a bug that was reported to Samsung, the new firmware should provide a fix. Most providers send firmware updates Over-the-Air automatically, but you have to download and install some updates from a computer using the USB cable.
If you purchased the phone used, the previous owner might have restored the moisture indicator with rubbing alcohol. In this case, the indicator would appear white even though it has been in contact with water.
Samsung's Standard Limited Warranty does not cover damage from "exposure to liquid, moisture or dampness."