It's often tempting, but most golfers are strong enough to resist the urge to stand behind another player's putting line to learn how his or her own putt might break.
To be clear, there is no penalty for doing so in standard stroke play if the other golfer is not your partner, but it's considered bad etiquette. You could walk in after the ball is in motion if you want to avoid getting a nasty look from the person putting.
When playing four-ball or foursomes, whether it's match play or stroke play, it is a penalty to stand on an extension of that line (Rules 22.6, 23.8), and you would get the general penalty: two shots in stroke play or loss of hole in match play.
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Now here's the wrinkle that could lead to penalties for both you and your partner. When your breach of this rule also helps your partner in some way with his or her next stroke, you both incur the same general penalty. Here's a scenario where this would happen:
You've got a 10-foot par putt and your partner has a 20-footer for birdie on the same line. You both strategize that your par putt would take some pressure off his or her birdie putt if you holed it, so you should putt first. You tell your partner to line you up for the putt by standing behind the hole to give you something to aim at. In this instance, you both would be penalized if you hit the putt since you both would benefit from the situation (you got something to aim at and your partner got a read for his or her putt).
Two other situations where partners would get the same penalty are if there is a breach of the 14-club rule or if you or your partner's breach did something to hurt your opponent's play.
Keep in mind that Rule 23.9 points out that in most cases, a penalty is only applied to the partner who violated the rule. In match play, for example, playing a wrong ball in four-ball match play would result in that player being eliminated from the hole, but the partner can still represent the side. In the case of penalty shots in stroke play, the strokes are almost always added to the player's score, not additionally to the partner's score.