Souls
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
Lesser souls give you soul points for the soul grid. 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.
Normal
Act 1
Corpsefire - Den of evil
Griswold - Tristram
Act 2
Fangskin - Claw Viper Temple level 2
The Summoner - Arcane Sanctuary
CHALLENGE LEVEL 30 - Mechanized Destroyer - Challenge Area in Tal Rasha's Chamber
Act 3
Sszark the Burning - Spider Cavern
Ismail Vilehand - Travincal
Act 4
Izual - Plains of Despair
Infector of Souls - The Chaos Sanctuary
Act 5
Shenk the Overseer - The Bloody Foothills
Lister the Tormentor - Throne of Destruction
Normal Resumé
You should finish normal with 12 souls. (10 from lesser souls, 1 from challenge lvl 30, 1 from Greater soul)
Nightmare
Act 1
Rakinishu - Stony Fields
The Countess - The Forgotten Tower Level 5
Act 2
Radament - Sewers level 3
Coldworm the Burrower - The Maggot Lair level 3
Act 3
Geleb Flamefinger - Travincal
Bremm Sparkfist - Durance of Hate level 3
CHALLENGE LEVEL 60 - The Swamp King - Challenge Area in Durance of Hate Level 3
Act 4
Hephasto the Armorer - River of Flame
Lord De Seis - The Chaos Sanctuary
Act 5
Eldritch the Rectifier - Frigid Highlands
Frozenstein - Frozen River
Nightmare Resumé
You should finish nightmare with 25 souls. (10 from lesser souls, 1 from challenge lvl 60, 2 from Greater soul and you start with 12 souls from normal)
You will most likely not finish challenge level 60 before hell, so 24 souls should be your goal here. Don't forget to come back for this soul!
Hell
Act 1
Blood Raven - Burial Grounds
The Smith - The Barracks
CHALLENGE LEVEL 99 - Stitches - Plaguelands
Act 2
Blood Witch the Wild - Halls of the Dead level 3
Fire Eye - Pallace Cellar level 3
Act 3
Toorc Icefist - Travincal
Wyand Voidbringer - Durance of Hate level 3
Act 4
Grand Visier of Chaos - Chaos Sanctuary
Act 5
Pindleskin - Nihlathak's Temple
Nihlathak - Halls of Vaught
Bartuc the Bloody - Throne of Destruction
CHALLENGE LEVEL 80 - Spawn of Ifrit - Worldstone Chamber
Challenges Recap
Challenge souls :
Act 2 Normal, Tal Rasha's Chamber - Level 30
Act 3 Nightmare, Durance of Hate Level 3 - Level 60
Act 5 Hell, Worldstone Chamber - Level 80
Act 1 Hell, Plaguelands, Burial Grounds - Level 99
Greater Souls
Act bosses each drop their greater soul, which is a socketable soul that you can put inside your Annihilus.
Normal :
Mephisto [1]
Nightmare :
Andariel
Baal
Hell :
Duriel [2]
Diablo
Rift Bosses :
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
Riftstones
Tier 1 Riftstones
Crazed Archer - Catacombs Riftstone
Vengeful blacksmith - Sewer Riftstone
Tier 2 Riftstones
Legacy's legend - Cave Riftstone
Mechanized destroyer - Crypt Riftstone
Tier 3 Riftstones
Fallen angel - Durance of hate Riftstone
Deathspeaker - Tomb Riftstone
Tier 4 Riftstones
Swampking - Maggot layer Riftstone
Guts - Dungeon Riftstone
Tier 5 Riftstones
Nemesis - Temple Riftstone
Guardian of terra - Worldstone Riftstone
Conclusion
There is 51 souls total to collect.