What's added to damage when throwing a two-handed weapon: the thrower's Strength modifier or the thrower's Strength modifier ×1.5 as for in melee?
No matter how many hands a typical creature uses to throw the thrown weapon, the typical creature only adds its Strength bonus to damage
The Player's Handbook on Thrown Weapons says, "The wielder applies his or her Strength modifier to damage dealt by thrown weapons (except for splash weapons…)" (113).
Compare this with Two-handed that says, "Apply 1-1/2 times the character’s Strength bonus to damage rolls for melee attacks with such a weapon" (ibid. and emphasis mine).
An exception to this is, for example, the extraordinary ability thunderous throw of the prestige class bloodstorm blade that, in part, says
[Y]ou[, a level 2 or higher bloodstorm blade,] can apply 1-1/2 times your Strength bonus to damage if you wield the thrown weapon with two hands, and you can use Power Attack with your thrown weapon attacks (adding two times the number subtracted from attack rolls as a bonus on damage rolls when throwing a two-handed weapon). (Tome of Battle 101)
Nonetheless, an exception like this is necessary for such a damage increase.
Just like a creature would apply 0.5x their strength modifier when making an off-hand attack with a thrown weapon, they would also apply 1.5x their strength modifier when making a two-handed attack with a thrown weapon.
I've been ruling according to the accepted answer for a long time. Today, however, I had a look through the Player's Handbook and have arrived at the opposite conclusion.
Source: Player's Handbook
Page 113 of the Player's Handbook, which was quoted in the accepted answer, says:
The wielder applies his or her Strength modifier to damage dealt by thrown weapons (except for splash weapons…)
It says nothing about two-handed attacks or off-hand attacks. The two-weapon fighting rules in page 160 also make no mention of the damage dealt, only of attack rolls:
Ranged Weapons: The same rules apply when you throw or fire a weapon from each hand. Treat a dart or shuriken as a light weapon when used in this manner, and treat a bolas, javelin, net, or sling as a one-handed weapon.
However, we CAN find rules that mention BOTH thrown weapons AND off-hand and two-handed attacks. These rules make no distinction for the strength modifier applied to melee or thrown weapons:
Strength (p. 8)
Damage rolls when using a melee weapon or a thrown weapon (including a sling). (Exceptions: Off-hand attacks [no distinction made for melee or ranged attacks] receive only one-half the character’s Strength bonus, while two-handed attacks [no distinction made for melee or ranged attacks] receive one and a half times the Strength bonus. A Strength penalty, but not a bonus, applies to attacks made with a bow that is not a composite bow.)
Damage (p. 134)
Strength Bonus: When you hit with a melee or thrown weapon, including a sling, add your Strength modifier to the damage result. A Strength penalty, but not a bonus, applies on attacks made with a bow that is not a composite bow.
Off-Hand Weapon: When you deal damage with a weapon [no distinction made for melee or ranged weapons] in your off hand, you add only 1/2 your Strength bonus.
Wielding a Weapon Two-Handed: When you deal damage with a weapon [no distinction made for melee or ranged weapons] that you are wielding two-handed, you add 1-1/2 times your Strength bonus. However, you don’t get this higher Strength bonus when using a light weapon with two hands (see Light, One-Handed, and Two-Handed Melee Weapons, page 113).
Damage (p. 135)
If you score a hit, roll damage and deduct it from the target’s current hit points. Add your Strength modifier on damage rolls involving melee and thrown weapons. If you’re using a weapon [no distinction made for melee or ranged weapons] in your off hand, add one-half your Strength modifier (if it’s a bonus). If you’re wielding a weapon [no distinction made for melee or ranged weapons] with both hands, add one and a half times your Strength modifier (if it’s a bonus).
I would contend that these rulings are more specific than the ruling given on page 113. This is because they explain what happens in the specific cases of wielding a weapon two-handed or in your off-hand, while the ruling in page 113 only talks about thrown weapons in general, without making a distinction between the different ways they can be thrown.
If you don't consider these rulings more specific, then you must also accept that off-handed thrown attacks gain 1x your Strength bonus, instead of 0.5x. That is, unless you can find another ruling talking about the damage dealt by off-hand attacks with thrown weapons.
Source: Rules Compendium
The Rules Compendium provides no further clarification. This is what it says on pages 150 and 151:
The Strength modifier on damage rolls applies to thrown weapons except for splash weapons.
What exactly does it mean by the Strength modifier on damage rolls? It's not talking about your strength modifier in general, but specifically the one that applies to damage rolls. I can honestly only assume that it is referencing the following:
LIGHT, ONE-, AND TWO-HANDED
(...)It indicates whether a melee weapon, when wielded by a creature of the weapon’s size category, is considered a light weapon, a one-handed weapon, or a two-handed weapon. This category also determines how a Strength bonus is applied on damage rolls.
Note that most thrown weapons are also melee weapons and are thus also categorized as light, one-, or two-handed.
Note 1: if you somehow manage to throw a two-handed weapon with only one hand, then you should only apply 1x your Strength bonus. This is according to RC, page 151:
If you’re allowed to wield a two-handed weapon in one hand, such as when riding and using a lance, that weapon is considered one-handed for the purpose of the Strength bonus on damage rolls while you’re using it in one hand.
Note 2: monster stat blocks can sometimes be used to figure out how a rule is supposed to be applied. It's unfortunate that a lot of the time they are inconsistent with each other or have errors. Here is a list of monster stat blocks that support each side of the argument (thanks to Hey I Can Chan for finding these):
- 1.0x strength modifier: tempest (MM4 109–10) and orc battlepriest (115)
- 1.5x strength modiifer: human commoner thoon thrall (MMV 111), stone giant's Rock Throwing says it uses both hands