It has always seemed to me that the omission of Tom Bombadil from Peter Jackson's movies is one of the least-minded changes. Out of all the characters in The Lord of the Rings, he is the one who, intentionally, fits in least with the rest. He's a great character and his section is in fact very moving in the book--but he's hard to imagine onscreen. Bright blue jacket, yellow boots, and singing half-random songs all the time? Yeah, maybe it's better to leave him out of the movie and leave him to imagination.
Going through Weta's books on the adaptations of The Hobbit, I noticed something about the way the teams were describing their treatment of Radagast the Brown. Radagast, as you know, is barely described by Tolkien, but they made him a fully-developed character for the movies. So many of the people who helped design Radagast said they really loved his character, and while some moviegoers liked him, others called him a great mistake. Someone even called him the Jar Jar Binks of this franchise.
I don't know. I'm mostly neutral to how they dealt with Radagast, given that Tolkien really didn't describe him much and also given that The Hobbit, stylistically, is a children's story where The Lord of the Rings isn't. But then the similarity between Peter Jackson's Radagast and Tom Bombadil struck me. Radagast has the bird nest in his hat instead of blue boots and he talks to animals instead of wandering the woods singing, but do you see the similarity in eccentricity? Both characters' eccentric traits are, further, connected to their relationship with nature. Both characters exist in nature instead of in society, and that is why they develop habits that outsiders find odd.
While the movies for The Lord of the Rings kept out the odd Tom Bombadil, The Hobbit brought in the odd Radagast. And I find that interesting.