Phil Shoemaker, a very experienced Alaskan brown bear guide, posts on the Fire as 458Win. He has said a 30-06 with 200 grain premium bullets is a good minimum. He has used many rifles as a guide but I believe he used a 30-06 as his backup rifle during at least one recent season.
Edit: I just saw Phil's post a few pages back. Looks like he now thinks a .270 w/ 150 G Nosler Partitions will do. I would listen to what he says which includes the idea that hitting the animal in the right place trumps caliber.
