From Diablo Wiki
Bounties are set tasks. For example, locate and kill a Superunique or Boss monster or complete an event or clear a dungeon and be rewarded with Experience, Gold and possibly a Rift Keystone. You access a Bounty by using the Waypoint map and selecting a waypoint marked with an exclamation mark (!) or Diablo's skull icon (indicating boss or quest boss). 
- There are 25 random bounties per game, 5 per act.
- You do not need to complete Campaign mode to access Adventure mode and Bounties.
- Rewards for completing Bounties are Rift Keystone Fragment which are used to open Nephalem Rifts. Also experience points and gold and Blood Shards which can be used to Gamble with Kadala.
- Blood Shards and Keystone Fragments are not awarded for completion of the first bounty in an each act.
- Bounties are not repeatable in the same game. You need to leave and begin a new game to refresh the bounties available.
List of Bounties in Diablo 3
The Achievements column lists any that are relevant to the specific dungeon visited or target monster killed or lore book the target monster may drop. The column does not include achievements earned for killing monsters you may run into along the way or passing through the main zone areas like Fields of Misery.
* = Target mob of the Bounty.
|Objective: Kill||Location||Can Drop Legendary Material||Towards Achievements||XP - Torment 1|
|Aspect of Anguish||Gardens of Hope||mat||achiev||5,800,000, 37,800, 2 bs, 1kf|
|Aspect of Hatred||The Silver Spire||mat||achiev||5,800,000, 37,800 2 bd, 1kf|
|Aspect of Lies||The Silver Spire||mat||achive||xp|
|Aspect of Pain||Gardens of Hope||mat||achive||xp|
|Aspect of Sin||The Silver Spire||mat||achive||xp|
|Diablo||Crystal Arch, The Silver Spire||mat||achive||xp|
|Izual||Great Span, The Silver Spire||mat||achive||xp|
|Kysindra the Wretched||The Silver Spire Level 1||mat||achive||xp|
|Khatun||Gardens of Hope 1st Tier||mat||achive||xp|
|Kao'Ahn||Gardens of Hope 2nd Tier||mat||achive||xp|
|Oah'Tash||Gardens of Hope 2nd Tier||mat||achive||xp|
|Pyres the Damned||The Silver Spire Level 1||mat||achive||xp|
|Rakanoth||Library of Fate, Gardens of Hope||mat||achieve||2,900,000, 18,880, 2 bs, 1kf|
|Rhau'Kye||The Silver Spire||mat||achive||xp|
|Slarge the Behemoth||The Silver Spire Level 1||mat||achive||xp|
|Sledge||Hell Rift||mat||achieve||5,800,000, 37,800 2 bs, 1kf|
|Torchlighter||Gardens of Hope||mat||achive||xp|
|Veshan the Fierce||Gardens of Hope 1st Tier||mat||achive||xp|
|Objective: Clear||Location||Can Drop Legendary Material||Towards Achievements||XP - Torment 1|
|Hell Rift||Hell Rift (2)||mat||achive||15,428,000 xp, 99,240, 2bs, 1kf|
|Objective: Cursed Event||Location||Can Drop Legendary Material||Towards Achievements||XP - Torment 1|
|The Cursed Chapel||The Silver Spire Level 2||mat||achieve||3,828,000, 25,960 0bs 0kf|
|The Cursed Dais||Gardens of Hope 1st Tier||mat||achive||xp|
Information below this point has been datamined from the Reaper of Souls PTR game files and as such should be considered a spoiler.
In one of the panels of images datamined called 'WaypointMap' are icons now known to be bounty indicators. All the images on the panel are in pairs, one plain and one with a green tick over it, probably indicating completion.
It does not necessarily mean that all of the icons represent a type of Bounty. All the icons are below.
|Bounty with a random boss, and the completed icon.|
|Bounty to complete an event, and the completed icon.|
|Bounty to clear a dungeon, and the completed icon.|
|Bounty with a quest or act boss.|
|This could be something to do with the Devil's Hand as the icons are similar to the image panel labelled Devil's Hand in the data files|
|This marks a completed bounty in a given act. When all five bounties are completed in a given act, a special random reward can be earned by visiting Tyrael in town.|
- Bounty Details - IncGamers' Gameplay Report, 08/11/13