Here in Colorado, I never really worry about critters. I've not seen a bear or lion, ever, although they say they're out there. Once I had a herd of maybe 10-12 elk come by my tent in the middle of the night during mating season. They were pretty adroit at going around my tent. A huge moose once patrolled the lake shore near where I was sleeping, grunting periodically to remind me that he was still around. It was sweet to finally hear him go, "Harr-UMPH!", which in moose-talk means something like, "There, sucker, I'm outta here, and I win."
But Yellowstone is a different story. The first few nights I have a terrible sleep. I hear everything, and there's a lot of critters roaming around at night (especially during a full moon, it seems). I have taken to popping a couple of Benedryl with my late dinner, and this lets me sleep straight through until morning. At Shoshone Lake last July I woke up and fired up my stove for my morning Joe on the beach. I noticed some tracks in the sand along the water's edge--the biggest griz tracks I've ever seen. It was nice of him to leave me alone while he strolled past in the middle of the night. I like bears that do that. If I wasn't slightly drugged, I probably would have heard him and freaked out.
I'm thinking that almost all critters will pass right by, if you don't bait them or otherwise pose a threat. But moose might be a different story altogether. They're so territorial, unpredictable, and goofy. Mice, raccoons, and other rodents might scour your campsite during the night, looking for food, and deer might come by to see if there might be a sweaty T-shirt that they can chew on for the salt, but none of these guys pose a personal threat to you.