Griphook is kind of an odd duck—er, odd goblin.
Up until being kidnapped at the end of the last film (and then rescued with Harry and the others), he worked at Gringotts (the Wizarding bank), and so Harry is super interested in getting his help in his Horcrux quest.
You see, Harry thinks that Bellatrix Lestrange has hidden a Horcrux in her vault, and he wants Griphook's help in breaking in to steal it.
Griphook is willing, but there's a catch: He wants the Sword of Gryffindor in return—which Harry needs in order to destroy any Horcrux they find. Harry tries to offer him gold, but Griphook isn't having it:
HARRY: I have gold. Lots of it.
GRIPHOOK: I've no interest in gold.
HARRY: Then what?
GRIPHOOK [Gesturing toward the sword]: That. That is my price.
So, Harry agrees—since what else can he do? He's not getting into the vault without Griphook, that's for sure.
Unfortunately, the wily goblin decides he's going to peace out mid-mission, leaving Harry, Hermione, and Ron battling all kinds of dangers in Gringotts:
GRIPHOOK: I said I'd get you in. I didn't say anything about getting you out.
Real nice, eh? Well, karma comes back to bite him in the butt: We later see him lying dead with the Sword of Gryffindor disappearing from his hand. Guess he should have stuck with Harry, who would have helped protect him from evil types, right?
(Oh, and fun trivia time: The actor who plays Griphook, Warwick Davis, also plays Professor Flitwick in the series.)