During Vesper's (clothed) Shower of Angst, Bond comes in to check on her. He sits down next to her, in the shower and asks if she's alright. When she says she can't get the blood (of a dead man) off of her hands, Bond sucks on her fingers (!) before asking her if she's cold. He adjusts the shower faucet to make the water warmer, and simply holds her.
After Bond wins the game, when he and Vesper are in the restaurant, he tells her he knows what her necklace means and that whoever gave it to her is "a very lucky man". Given that the film's established that Bond pursues women to one-up other men ("You're not my type." "Smart?" "Single."), his implicit statement that he's not going to pursue Vesper any more and will respect that she loves someone else is very meaningful.
"I have no armour left. You've stripped it from me. Whatever is left of me - whatever I am - I'm yours." This is one of the very few times in the entire film series where you can un-ironically say: "Ohh, James..."
An out of universe example: almost everyone was hating on Daniel Craig as Bond, that's when Sean Connery, Roger Moore, Timothy Dalton and Pierce Brosnan all came forward to give their support.