The sneak attack of the rogue

[WinterIsComing]

If the rogue has several attacks ==> do the rogue’s attack deals extra damage any time her target would be denied a Dexterity bonus to AC (whether the target actually has a Dexterity bonus or not), or when the rogue flanks her target ? Or just the first attack ?

[tstewt1921]

"The rogue’s attack deals extra damage any time her target would be denied a Dexterity bonus to AC (whether the target actually has a Dexterity bonus or not), or when the rogue flanks her target. This extra damage is 1d6 at 1st level, and it increases by 1d6 every two rogue levels thereafter. Should the rogue score a critical hit with a sneak attack, this extra damage is not multiplied."

Your DM may rule differently but as worded, if you are flanking or they are denied their dexterity bonus, you get sneak attack, and this would be every attack.

[tyckspoon]

Sneak Attack applies any time its triggering conditions are met; there is no per-round limit.

If there is something happening that will cause it to only happen on the first attack, it's usually because the Sneak Attack is being enabled by something that is a temporary condition. For example, if you are Hiding or Invisible and can only Sneak Attack because your target can't currently see you, then when the Rogue makes that first attack he will (usually) become detected, no longer denies his target Dexterity bonus, and so can't Sneak Attack them again.

[HouseRules]

Sneak Attack
If a rogue can catch an opponent when he is unable to defend himself effectively from her attack, she can strike a vital spot for extra damage.

The rogue’s attack deals extra damage any time her target would be denied a Dexterity bonus to AC (whether the target actually has a Dexterity bonus or not), or when the rogue flanks her target. This extra damage is 1d6 at 1st level, and it increases by 1d6 every two rogue levels thereafter. Should the rogue score a critical hit with a sneak attack, this extra damage is not multiplied.

Ranged attacks can count as sneak attacks only if the target is within 30 feet.

With a sap (blackjack) or an unarmed strike, a rogue can make a sneak attack that deals nonlethal damage instead of lethal damage. She cannot use a weapon that deals lethal damage to deal nonlethal damage in a sneak attack, not even with the usual -4 penalty.

A rogue can sneak attack only living creatures with discernible anatomies—undead, constructs, oozes, plants, and incorporeal creatures lack vital areas to attack. Any creature that is immune to critical hits is not vulnerable to sneak attacks. The rogue must be able to see the target well enough to pick out a vital spot and must be able to reach such a spot. A rogue cannot sneak attack while striking a creature with concealment or striking the limbs of a creature whose vitals are beyond reach.

Read the emphasized part.

[Psyren]

If the rogue has several attacks ==> do the rogue’s attack deals extra damage any time her target would be denied a Dexterity bonus to AC (whether the target actually has a Dexterity bonus or not), or when the rogue flanks her target ? Or just the first attack ?

It applies to every attack that meets the conditions. For flanking, this means that you can generally get your whole attack sequence off, since the condition that enables "flanking" is based on position, and targets usually can't move when it's not their turn. Conversely, it means that "invisible" and "hiding" might only give you one attack, since the most common sources of those conditions break after that first attack.

[King of Nowhere]

And while an inexperienced DM may feel it too much and require a nerf for it, it's not broken. A rogue sneak attacking deals about as much damage as a barbarian with power attack. To make multiple attacks, the rogue needs to stand still, and rogues are squishy.
Yes, in the right conditions a rogue can deal huge damage, but they require proper setup, and have drawbacks.

[Troacctid]

Rules Compendium clarifies that yes, you can do it on every attack.

Precision damage applies on any attack that meets the requirements of the ability that grants the damage. This includes multiple attacks made during a full attack. If conditions somehow change between multiple attacks, attacks that not longer meet the ability’s requirements can’t deal precision damage.
However, there are two exceptions. First off, if multiple attacks are made in one action, it has to be a full-round action in order to get sneak attack on any of the attacks after the first.

A form of attack that enables an attacker to make multiple attacks during an action other than a full-round action, such as the Manyshot feat (standard action) or a quickened scorching ray (swift action), allows precision damage to be applied only to the first attack in the group.
Second, if the attack in question is a spell, only the first attack made by that spell each round is eligible for sneak attack (or any other bonus to damage, e.g. Point Blank Shot).

Some weaponlike spells can strike multiple times in the same round. When the caster receives a bonus on damage rolls or some form of extra damage (such as precision damage) with such spells, the extra damage applies only on the first attack, whether that attack hits or not.

[Mordaedil]

It is pretty satisfying to play a rogue/warblade and score 7 hits with two-weapon fighting with a 8d6 sneak attack with two shortswords.

So many d6's...