At what quests/points in time do each of Deckard Cain's talk options become available?

Solution 1:

Available Dialogues in Diablo 3 for Deckard Cain

Who Are You?

Available at the start of the quest: A Shattered Crown

Prophecy of the End Days

Available at the start of the quest: A Shattered Crown

Your Adopted Niece

Available at the start of the quest: A Shattered Crown

Mad King Leoric

Available at the start of the quest: A Shattered Crown Disappears at the start of Sword of the Stranger

The Mysterious Stranger

Available at the start of the quest: Sword of the Stranger Disappears at the start of the Broken Blade *Not needed for conversation achievement.

The Archangel Tyrael

Available at the start of the quest: Sword of the Stranger

The Horadrim

Available at the start of the quest: The Broken Blade

Origins of the Coven

Available at the start of the quest: The Broken Blade

The Worldstone

Available after the end of the quest: The Broken Blade Inaccessible at the start of The Doom of Wortham. *NOTE: You can use the quest choose method to start at the beginning of Doom of Wortham, just don't talk to The Stranger, since when the quest officially starts, Deckard can't be talked to anymore.

Leah and Cain's Travels

Available after the end of the quest: The Broken Blade Inaccessible at the start of The Doom of Wortham. *NOTE: See above for details about the last 3 convos.

Taken from http://soe.hubpages.com/hub/Deckard-Cain-Lore-and-Character-Dialogue-Guide-Diablo-3

Solution 2:

I did a run through with a new character, noting when each of the conversations became available. There are a few that the exact point in the quest is not 100% because a friend joined and I didn't want to hold them up by running back after every single objective. Once you've heard a conversation, if it was missable, it seems to stay around in stead so until I go through with another character and don't talk to anyone, I can't be certain when exactly they can be missed.

Deckard Cain's conversations are only in Act I and since you can't speak to him after he enters his house once The Doom in Wortham starts, that's definitely when all conversations with him have certainly been missed.

Act I

• Who Are You?: Available after accepting the quest A Shattered Crown.
• Prophecy of the End Days: Available after accepting the quest A Shattered Crown.
• Your Adopted Neice: Available after accepting the quest A Shattered Crown.
• Mad King Leoric: Available after accepting the quest A Shattered Crown.
• The Mysterious Stranger: Available as part of the end of Reign of the Black King.
• The Horadrim: Available after accepting the quest Sword of the Stranger.
  • The Archangel Tyrael: Available after hearing the conversation The Horadrim.
• Origins of the Coven: Available from the time after you complete the quest Sword of the Stranger and before you accept the quest The Broken Blade.
• Leah and Cain's Travels: Sometime during the quest The Broken Blade. It might be related to Leah's conversation Leah's Childhood so I'll have to do some testing.
• The Worldstone: Sometime during the quest The Broken Blade I don't have the specific objective on this one.
  • Destruction of the Worldstone: Available after hearing the conversation The Worldstone.