Oh, and I just happened to turn to this bit of head canon in my R/S notebook, and couldn't resist adding it:

Re their relationship with Hagrid: James and Sirius immediately took to him at Hogwarts because he went into the Forbidden Forest and was therefore Cool. Remus, however, stayed away from him. He knew of Hagrid's love of magical creatures, and he thought that Hagrid would probably figure out his secret. Not that he didn't trust him, but he knew how Hagrid accidentally let slip things. He also didn't fancy Hagrid trying to make a pet of him!