At the end, when the Dragon’s dead and word has spread, the folks of Laketown show up to claim his hoard, assuming Bilbo and the Dwarves are dead. All fine and dandy, they DID lose their town by the dragon so perhaps are owned some money. But the Elves show up too, and I never got that apart from setting up the big battle. They had no stake in Smaug’s treasure and no real business being there. Thorin was well with his rights to tell them to jump in the nearby Lake. Why did the Elves come to the mountain?
Bard, the Laketown man who slew Smaug, and took over, asked the Wood Elves for help. Laketown is destroyed. Winter is coming. The Men and Elves go to the mountain. However, Thorin is not about sharing any of it. Bilbo - secretly - has the very valuable Arkenstone and gives it to Bard & Elvenking as a bargaining chip. So that is used to get (to Thorin’s super-ire) Bilbo’s 1/14 share - which is still pretty good for the Men & Elves - and they’re about to depart. Then the Orcs arrive. And they want it all too.
Thranduil the King of the Wood-elves did think he was entitled to some part of Smaug’s treasure, both for coming to the aid of Bard (who slew the dragon) and as reparation for Smaug’s depradations over the years.
Plus he just kinda liked treasure, “especially silver and white gems”. He was going to the Mountain in the first place, after learning of Smaug’s death, because he figured the Dwarves would be dead and the treasure un-owned and unguarded.
I’ll stand corrected, Kimstu
(had to pull out my book to review)
Elvenking was already on his way to the Mountain, when he met up with Bard and his folk. And only then did he decide to help the Laketown folk out a little. Then they went to the Mountain.
I hope (but do not expect) the movie to depict Elvenking as a Mr. Burns-esque greedy ol’ bastard. His look in Rankin & Bass cartoon was spot-on.
Elves are as greedy as any other race. Exhibit A: The Silmarils
I remember the “silver and white gems” line (for no good reason), but what depredations? I had thought Smaug flew in and ate the dwarves, maybe buzzed and fewmetted on Laketown, and then settled in. Did he attack Mirkwood? Or did they mean disrupting trade?
If you can’t tell, I really like Smaug. 
Thranduil always seemed to me to be an odd sort of character - on the one hand, he loves nature and the woods, and while avoiding the dwarves lost in the woods, they were fairly patient with the interlopers. He is noble towards the Lake-folk after their town is destroyed. In the end, he treats the fallen Thorin with high honour.
On the other hand, he is high-handed towards the captured dwarves, desires jewels, gold and mithril, and is prepared to fight for such things (or claim treasure that was lying around after the death of the dragon).
I think Tolkien had not quite sorted elves out in his head. The woodelves seem to me to reflect more of faerie lore than his own. Legolas, the son of Thranduil demonstrates few of the traits of his father.
Si
I would say that Legolas is no more representative of Elves as a whole that Gimli of Dwarves, Aragorn of Men, or Frodo of Hobbits. They all represent the best the races have to offer.
I think another part of the disconnect between the portrayal of Thranduil in The Hobbit and other portrayals of Elves in the legendarium is that many of the other portrayals are from Elven points of view, whereas The Hobbit is written by Bilbo.
Because the elves are dicks.
That’s pretty much Terry Prattchett’s take, anyway.
Thranduil remembered the sack of Doriath, where the dwarves plundered the treasures of Thingol and ran off with the nauglamir, which contained a silmaril.
So that probably helped him justify deserving a share of the treasure.
Elves have long memories.
OK, so Feanor took the theft personally and led some Elves to kinslayer acts.
But that doesn’t represent the entire race.
Cirdan gave his Ring of Power to Gandalf.
Galadriel turned down the One Ring.
All Elves are dicks, but some aren’t complete dicks, but only semi-dicks. Quasi-dickish. The Diet Coke of dickishness.
Yay fewmets! 
I don’t know of any specific losses that the Elves sustained under Smaug, but IIRC doesn’t Thranduil say something at some point about “what we have suffered” from him? I may not RC, though.
Anyway, I would totally believe that Smaug scooped up the occasional Wood-elf messenger or convoy carrying valuables, and that Thranduil would consider that a justification for going up to the Mountain once he knew Smaug was dead to reclaim some property—and as for anything else that happened to be lying around in the lair, well, finders keepers, right?
I never said all Elves are greedy, just that they’re not any more immune to greed than any other race
So did Sam and Faramir. Your point?
Why didn’t Bilbo just give them his 1/14 share himself?
Because Thorin wouldn’t have let him.
In his eyes, he did. Thorin told him he could take first pick, and so he picked something small enough that he could carry it himself out to the elves and humans. A fourteenth share of gold or other more conventional wealth would have been many wagonfuls, not something to sneak out with in the middle of the night.
Well, he also picked something he knew Thorin wanted, which seemed kinda dickish.
I thought he grabbed the arkenstone on one of his scouting trips and then when he got back up the secret passage, Thorin told him specifically about the Arkenstone.