On my third time seeing The Hobbit, I paid more attention to the score than I had before. As in the score to LOTR, Shore uses leitmotifs in a deliberately Wagnerian manner, and I was able to figure out and follow a few of them through their development. The most prominent is the Song of the Lonely Mountain, which the dwarves sing in Bilbo’s home and the melody of which becomes a major recurring theme. There are also clear themes for Thorin and Erebor that come up a lot.
I’m less sure about the themes that come up less often, such as for Radagast, his rabbits, the Arkenstone, Sting (whose theme may just be a minor second “sting” in the music), and so on. I think there may be a general sword theme, and maybe a theme representing the diaspora of the dwarves after the fall of Erebor.
There are themes carried over from LOTR, too — the Shire, the Ring, and so on. One lovely touch (among many, really): When Bilbo evades the question of how he escaped from the goblins, Gandalf clearly suspects something, and in the music the Ring theme starts and then stops, uncompleted, telling us that Gandalf thinks briefly about the One Ring, but then puts aside the thought.