A small thing, but Balin's friendship with Bilbo. He's the only one who would go with Bilbo part of the way into Smaug's lair and even carried him back out. In the epilogue, Balin visits Bilbo in Bag End and they happily reminisce over the old times together.
Some of this carries over into The Lord of the Rings, in a more tragic way. When the Company of the Ring find Balin's burial site in Moria, Frodo thinks back to Balin's Shire-visit, and Gandalf is saddened at the prospect of bringing the news of his death back to Bilbo.
In the books, Dori was always the one who carried Bilbo and made sure he was safe, even climbing down a tree when the wargs attacked to boost Bilbo up to safety!
This line in the last chapter.
... and though many shook their heads and touched their foreheads and said "Poor old Baggins!" and though few believed any of his tales, he remained very happy to the end of his days, and those were extraordinarily long.
Although it's not quite as explicit as in the movie, Thorin's friendship and later reconciliation with Bilbo even though that was a Tear Jerker due it being on Thorin's deathbed were quite touching considering howdifferent the two were. Particularly nice is when Bilbo is complaining about how dreary Erebor is and Thorin laughs and tells him to wait until it's been cleaned and redecorated, implicitly inviting Bilbo to stay or return at some point to see Thorin's kingdom restored to glory.
What about the Elvenking's response to Bilbo giving up the Arkenstone to attempt to keep things civil? He's the first to ask Bilbo not to return to the Dwarves, explicitly because he was worried that Thorin wouldn't react well when he found out what Bilbo had done (and as it turns out, the Elvenking was right to worry). The Elvenking isn't the nicest, most altruistic character in the book, but this scene is downright redeeming.
Bilbo attempting to avert the war by giving away the Arkenstone in the first place, claiming it as his share of the treasure (a shaky claim based on Exact Words, but not an unreasonable one). Bilbo, of his own volition, was willing to give up his entire share of the reward for all he's been through just to try to keep the peace. It doesn't work, but it was a noble effort.
The Elvenking ignores a dragon hoard he believes to be unguarded, to provide relief aid after the wreck of Laketown. He doesn't even just send the baggage train - he diverts his entire army to help. One of the most altruistic acts in the Tolkien canon, and very few readers seem to even notice it.
He's also the only one who hesitates to openly go to war over the gold of Erebor. "Long may I tarry, ere I begin a war for gold," are his exact words.
A little moment when the company have been imprisoned in Mirkwood; Thorin has been separated from the others, has had no contact with any of them for days and become "too wretched to be angry any longer." And then he hears Bilbo's voice at his keyhole and his spirits immediately revive.
Frodo, out of nowhere, singing a song that takes Gandalf by surprise:
The Road goes ever on and on Down from the door where it began. Now far ahead the Road has gone, And I must follow, if I can, Pursuing it with eager feet, Until it joins some larger way Where many paths and errands meet. And whither then? I cannot say.
Gandalf: My dear Bilbo! Something is the matter with you! You are not the hobbit that you were.
In general, the movie as a whole is pretty lighthearted. The filmmakers somehow manage to make Bilbo as adorable and friendly as possible, not just with his Ugly Cute character design, but also with his friendly and somewhat naive personality. He risks himself to save the dwarves by fighting the spiders. Then he also takes a greater risk by infiltrating the wood-elves palace to save the dwarves again.note While he did steal Gollum's ring, he initially took it because he thought it was merely a random ring and thus he wanted to took it as a souvernir. And later Gollum wanted to eat him, so Bilbo takes and uses the ring to escape.