What does Thorin vow to do anyone who withholds the Arkenstone in The Hobbit?

Thorin vows to get revenge on anyone who keeps the stone from him.

The Arkenstone is very important to Thorin.  It is his birthright.  To him it is the most valuable jewel of all of the dwarves’ riches hidden in the mountain.  It hurts him deeply that the dragon has it.  It is one of the reasons he wants to go into the Lonely Mountain to get it.

"The Arkenstone! The Arkenstone!" murmured Thorin in the dark, half dreaming with his chin upon his knees. "It was like a globe with a thousand facets; it shone like silver in the firelight, like water in the sun, like snow under the stars, like rain upon the Moon!" (Ch. 12)

When the dwarves do take the mountain, Bilbo finds the stone.  He knows what it is from the description, but he does not tell Thorin immediately.  He thinks he can use the stone to negotiate with the elves and men who are at a standoff with the dwarves. 

Bilbo becomes concerned about Thorin’s reaction to the stone being missing.  He worries about dragon-sickness, or the dwarves’ reactions to the gold, specifically Thorin’s.  The longer Bilbo holds out, the more worried he gets.  He knows that Thorin will be very, very angry if he tells him he has had it this whole time.

"For the Arkenstone of my father," he said, "is worth more than a river of gold in itself, and to me it is beyond price. That stone of all the treasure I name unto myself, and I will be avenged on anyone who finds it and withholds it." (Ch. 16)

Poor Bilbo feels bad about withholding the jewel from Thorin, even though he is also a little nervous about the fact that Thorin has vowed revenge on anyone who withholds the stone.  When Thorin finds out he is mad, and threatens to throw Bilbo off the mountain.