Bilbo takes the Arkenstone. He isn't entirely sure why he does it, but he picks it up and knew exactly what it was. He had some idea it might be of use later on.
Biblo 'borrows' the Arkenstone.
A gold two-handled cup.
a golden cup
The Arkenstone
Bilbo took the Arkenstone. It was the treasure Thorin desired most.
He says they want revenge.
Bilbo found the Arkenstone in Smaug's treasure chamber.
Bilbo claimed that under the terms of the contract he was due a proportion of the dragon's treasure, and that he had taken the Arkenstone as his share.
Treasure from Lonely Mountain (gold and silver for Bilbo).
Bilbo took the Arkenstone. It was the treasure Thorin desired most.
When they first get to the treasure trove. Thorin gives it to Bilbo as part of his payment.
The huge hoard of treasure that Smaug owned took away Bilbo's breath. And specifically the Arkenstone.
In the beginning it was Smaug , then in the end of The Hobbit , Bilbo gains it
Dwarves had a bad habit of lusting after gold and treasure. Bilbo felt the desire burning in his heart when he saw the mounds of treasure in front of him.
He says they want revenge.
Bilbo found the Arkenstone in Smaug's treasure chamber.
He was thankful towards Bilbo as he had just received the greatest treasure in that can be found in the Lonely Mountain and was now able to try make a deal with Thorin Oakensheild for a share of the treasure to rebuilt lake town.
Bilbo claimed that under the terms of the contract he was due a proportion of the dragon's treasure, and that he had taken the Arkenstone as his share.
Bilbo brought back a magical ring, several chests of treasure, and most importantly, the Arkenstone, a precious gem that was a symbol of the dwarves' alliance.
Because during the unexpected party, Thorin promised Bilbo 1/14th payment of the treasure in return for Bilbo's services as a 'thief'. Though Bilbo did not do much in the way of being a thief, he did save the dwarves from Thranduil, as well as help them gain entrance into the mountain. They also wanted him on the journey because it would have been unlucky to take on their journey with 13 members. At the end of their adventures, Bilbo had obviously earned his 1/14th share, so Thorin fulfilled his promise and sent Bilbo home with a chest of treasure (though it is hinted later on in LotR that Bilbo ended up receiving more).
He has no need for more