How can I find out if a device has a vibrator?

The Vibrator class does just that. It's hasVibrator() method returns a boolean indicating if vibrating is supported.

1. Get an instance of the Vibrator class which is a system service.
2. Query the Vibrator class using the hasVibrator() method.

String vs = Context.VIBRATOR_SERVICE;
Vibrator mVibrator = (Vibrator)getSystemService(vs);

boolean isVibrator = mVibrator.hasVibrator();

This may help for API<11:

Context.getSystemService() returns a service object or null if no service.

if ( getSystemService(VIBRATOR_SERVICE) != null ) {
    //Vibrator exists
}