Specials: The strength modifier is added to most melee attack and damage rolls, both subject to provisions detailed below. The strength score is used to determine how much weight a character can carry before becoming encumbered.
Strength tends to be of some importance to all characters, as encumbrance limits can be a major irritation, and the limits for the lowest strength scores are not always sufficient for what some players consider "normal" gear, much less that gear plus the loot to be carried out of a dungeon. For characters who focus on melee combat, though, strength is of greater importance, as a high strength causes more hits and more damage per hit. As a result, strength-based characters (those striving for as high a strength as feasible, once the other abilities are at acceptable levels) tend to be good choices for new players and those who prefer to keep the game simple, as well as those who just enjoy the massive damage. Even those who take a different approach to melee combat (such as the more defensive dexterity-based approach) generally find value in strength for the bonus to damage.
While the strength modifier is normally added to melee attack rolls, weapon finesse allows the dexterity modifier to be used instead if certain weapons are being wielded.
The bonus to damage from strength can be affected by several considerations. The "normal" situation is adding the strength modifier to damage inflicted by a melee weapon or by certain thrown weapons (specifically, darts and throwing axes). Other ranged weapons place a limit on how much of the strength modifier can be added to damage, often preventing any addition at all; see mighty. Furthermore, a two-handed weapon, excluding double-sided weapons, adds 1.5 times the strength modifier to damage, while an off-hand weapon adds only half the modifier. (Fractions are rounded down.) Double-sided weapons are a special case because their ends are treated separately, with hits from the main-hand side adding the (full) modifier to damage, and hits from the off-hand side adding half the modifier. Another consideration (besides the type of weapon used) is that the game engine forces each successful hit to inflict at least one point of physical damage, so there is a limit to how much a negative strength modifier can impact damage.
One consequence of the way strength modifies damage for different types of weapons is that a character with lower strength tends to inflict more damage when dual-wielding, while one with a higher strength tends to inflict more with a two-handed weapon. The dividing line between these cases is not simple to specify, but it is related to how the strength modifier compares to the damage from other sources (e.g. base damage of the weapon).