Most off-line putts can be traced to the same simple fault: Allowing your head to move during the stroke. When your head moves, because you're either watching the blade or the ball, your body also moves slightly, changing the path of the clubhead so the ball is either pushed or pulled off the intended line. Take heart, even the pros wrestle with this fundamental mistake.
Some players move their heads because they want to watch the ball roll the entire way to the hole. There are several ways to hold your head still until after impact: Retain the position of your spine throughout the stroke while your shoulders swivel around it (if the spine stays still, the body and head will, too). On short putts, listen for the ball to drop in the hole instead of trying to watch it. Keep your head in place until the putterhead has moved past your right ear.
Head movement also may be the result of trying to watch the putterhead swing back and through. Shift your focus from the putter to the ball. Turn the ball so the label is in back and stare at it until after contact.
Another cure for the bobbing head is not to look down at all, but to swivel the head so it's trained on the target throughout the stroke. This is a radical solution -- Tom Kite was using it earlier this year -- but one that might work as a way to freeze your head and body while also ingraining good rhythm and tempo in your stroke.