Certain super unique monsters in certain difficulties are able to drop their soul on death. There are two tiers of soul drops, lesser souls and greater souls.
To collect both the greater souls and the lesser souls you must click on the soul object that drops when you kill the monster.
Lesser souls give you small passive bonuses on your Annihilus. Typically there are 2 per act per difficulty, usually dropped from super unique monsters related to a quest. There are also other lesser souls available from challenges and other custom content.
Corpsefire - Den of evil (5% fire resist)
Griswold - Tristram (500 defense)
Fangskin - Claw Viper Temple level 2 (5% lightning resist)
The Summoner - Arcane Sanctuary (5% faster cast rate)
Mechanized Destroyer - Stony Tomb level 2 (5% chance of staggering blow)
Sszark the Burning - Spider Cavern (5% fire resistance)
Ismail Vilehand - Travincal (5% Increased Attack Speed)
Izual - Plains of Despair (+50 to life)
Infector of Souls - The Chaos Sanctuary (10% faster hit recovery)
Shenk the Overseer - The Bloody Foothills (5% summoned minion damage and life)
Lister the Tormentor - Throne of Destruction (5% magic resistance)
Rakinishu - Stony Fields (5% run speed)
The Countess - The Forgotten Tower Level 5 (5% poison resistance)
Radament - Sewers level 3 (5% poison resistance)
Coldworm the Burrower - The Maggot Lair level 3 (5% cold resistance)
Geleb Flamefinger - Travincal (10% elemental damage)
Bremm Sparkfist - Durance of Hate level 3 (5% lightning resistance)
The Swamp King - Swampy Pit level 3 (5% all resistances)
Hephasto the Armorer - River of Flame (500 defense)
Lord De Seis - The Chaos Sanctuary (10% physical damage)
Eldritch the Rectifier - Bloody Foothills (5% run speed)
Frozenstein - Frozen River (5% cold resistance)
Blood Raven - Burial Grounds (5% minion damage and life)
The Smith - The Barracks (500 defense)
Blood Witch the Wild - Halls of the Dead level 3 (10% physical damage)
Fire Eye - Pallace Cellar level 3 (5% run speed)
Toorc Icefist - Travincal (10% elemental damage)
Wyand Voidbringer - Durance of Hate level 3 (+50 to mana)
Grand Visier of Chaos - Chaos Sanctuary (5% magic resistance)
Pindleskin - Nihlathak's Temple (5% run speed)
Nihlathak - Halls of Vaught (10% minion damage)
Bartuc the Bloody - Throne of Destruction (5% chance to bleed)
Spawn of Ifrit - Icy Cellars (5% missile speed)
Challenge souls :
- Act 2 Normal, Stony Tomb, Rocky Waste, max level 30. Time limit: 3 minutes
- Act 3 Nightmare, Swampy Pits, Flayer jungle, max level 60. Time limit: 4 minutes
- Act 5 Hell, Icy Cellar, Ancients Way, max level 80. Time limit: 2 minutes 20 seconds
Act bosses each drop their greater soul, which is a socketable soul that you can put inside your Annihilus. Mephisto's soul drops in normal, Andariel and Baal in nightmare, and Duriel and Diablo in hell.
All rift bosses also drop a greater soul. Currently these are:
- Trang'Oul, located in Hell Act 1, Cathedral, min lvl 75.
- Ctoggha, located in Hell Act3, Disused Reliquary, Kurast Causeway, min lvl 75.
List of Greater Souls and their bonuses can be found in this page: Uniques/Greater Souls