I've had elk approach me at Yellowstone. I was fishing the Madison a couple of months ago, and a dozen elk waded the river right in front of me (within 50m). They generally ignore people in Yellowstone, likely because encounters are so common.
I also nearly hooked a Mule Deer on a backcast before I noticed it. I was fishing Slough Creek below the campground in YNP, and the deer walked up behind me on the bank before I saw it. I didn't miss it by more than a foot.