I've got several.
Had bears on two different trips to New Mexico in Cimarron Canyon. One trip, the group next to us left food out in plastic containers. Its tough to sleep at 4:00 am with bears in the next site ripping it apart. Needless to say they had a mess to clean up.
Second time, a year later - same area, was a bear just wandering through the camp ground after dark. I met him at the front of my truck (at about 5 feet). I almost accidently......He headed away and acted more annoyed than scared. I about had a heart attack.
Had a skunk in Texas wander down a trail I was hanging over in a net hammock one night. Heard something and smelled skunk. Just laid as still as I could. I assume he winded me as he went back the way he came at a high rate of speed. Luckily, I didn't get sprayed...Lesson learned, don't hang over a game trail no matter how small it is.
My favorite critter story is from fly fishing in South Dakota. I was up the canyon a good mile or two and alone (spooky factor had set in for some reason and I was already on edge). I was walking up on the hill looking down on the creek for holes to fish (the grass/brush at the creek was over my head). Found what looked to be a nice hole and made my way down into the grass. About halfway through it, something jumped up right in front of me and took off, I about jumped out of my boots and ended up on my back with tackle scattered everywhere. I was on the ground before my brain registered "Doe". I think she laid there as long as she could hoping I'd pass her up. I about stepped on her. I often wonder who was spooked the most out of the deal and get a good chuckle out of it now.