baldursgate

All characters get at least one attack per round (APR), but there are a number of bonuses that can increase than number:

The max APR is capped at 5, though that can be exceeded through the use of temporary effects. APR bonuses are multiples of 1/2. A 1st level warrior (1 APR) wielding a single long sword with which he is specialized (+1/2 APR or 0.5) will have 1.5 attacks per round. The game will display this as 3/2, meaning 3 attacks over 2 rounds.

Class

Most class groups get a single attack per round. Warriors (Fighters, Paladins, Rangers) and Monks get an extra +1/2 attack at levels 7 and 13. Warriors may get additional bonuses based on their level of proficiency with their main-hand weapon (see following table). Monks also gain +1/2 APR at levels 4, 10, 16 and 19 when fighting unarmed, maxing at 4 apr at level 19.

Warrior APR Bonus by Level and Proficiency [1]
Warrior Level Unskilled (0) Proficient (1) Specialized (2) Master (3) High Master (4) Grand Master (5)
BG1 BG2 Enhanced Editions two letters logoBaldur's Gate I & II: Enhanced Editions
This icon indicates content from all Enhanced Editions of the Baldur's Gate games. May situationally encompass Siege of Dragonspear and The Black Pits I & II content as well.
1 1 3/2 5/2 3/2 2
7 3/2 2 3 2 5/2
13 2 5/2 7/2 5/2 3

While some non-warrior classes can also advance to specialized or higher (e.g. Swashbuckler), they do not gain more APR from this, only THACO and damage bonuses.

Original games two letters logoBaldur's Gate I & II Classic
This icon indicates content from all original Baldur's Gate games, extensions included.
Note: No known method makes it possible for player characters to achieve grand mastery in the original BG1 even with Tales of the Sword Coast, but enemies do benefit from it.

Enhanced Editions two letters logoBaldur's Gate I & II: Enhanced Editions
This icon indicates content from all Enhanced Editions of the Baldur's Gate games. May situationally encompass Siege of Dragonspear and The Black Pits I & II content as well.
Note: A dual-classed Fighter-Druid or Fighter-Thief can achieve grand mastery within the 161,000 XP cap of BG:EE, but the 5th proficiency point can only be added once one class levels up to at least 9.

Effects

Several effects can increase a character's APR:

Weapons

Weapons all have a Base APR assigned to them, and almost all melee weaponry like spears, swords or flails have a base APR of 1. The base APR is the lowest, or bottom value of the weapon's APR. That value can be modified by weapon proficiency skills or other effects, such as certain spells, innate abilities or worn items. Dedicated missile weaponry like darts or bows typically have a higher base APR value assigned (exception would be crossbows).

The following ranged weapon types set the base APR of the weapon to 2 or 3:

Note:If the wielder has sufficient pips in a missile weapon proficiency type, then the extra APR will be added to the base APR

The magical weapons listed below add an additional attack per round to the wielder in melee. All those weapons are edged, so Cleric and Fighter / Cleric have no way of increasing their APR via weapons. Kundane, Belm and Ninjatō of the Scarlet Brotherhood can be equipped in either hand, but only the main hand gets the extra APR (so if dual-wielding, a more powerful weapon may be held in the main hand). The throwing daggers used in melee, however, can only be equipped in the main hand, but allow wielding another melee weapon in the off-hand. Weapon proficiency modifiers still apply. Two of those weapons can be dual-wielded at the same time, for overall 4 base APR.

The weapons created by spells or abilities listed below set APR to a certain value, which can then be increased by effects such as Haste but are unaffected by weapon proficiency skills.

The Gauntlets of Extraordinary Specialization provide a bonus +½ (0.5) APR.

In Original BG2 only, the following sources grant Weak Haste:

Dual Wielding

Wielding an offhand weapon adds an additional attack per round with that weapon. All other attacks will be by the main hand.

Shapeshifting

When shifting form into another creature, the new one will override base APR. Those are cumulative with the bonuses from Warrior levels and haste effects, but override equipped weapons. Examples:

APR penalties

Certain debuffs can also lower attacks per round:

Cleave Mechanic/Bug

The game possesses a hidden "cleave" mechanic (or maybe it's a bug) that allows a character to perform more attacks per round than they're supposed to by (seemingly) granting an extra attack per enemy killed if another enemy is nearby.

There seems to be some kind of limit/additional requirements for this to happen, but it potentially allows a character to attack significantly more in a single round than normal, as evidenced by this test footage of a Kensai with only 2 APR being able to do 6 critical strikes against 6 werewolves with a single cast of the ability (which lasts exactly 1 round).

References