It's not animals you really need to worry about, it's bugs. I pack a tent to keep out of the bugs more than I do to keep the critters out. The only time I can ever remember having issues with animals was in the Ptolemy Plateau, for some reason there were a lot of gophers, and they were all over our campsite at night, scratching at the walls of out tent and even trying to come up from underneath. We spent the night playing whack-a-mole. The small critters that will approach your bed at night don't pose any risk, they're just a serious annoyance while you're trying to sleep.
Bears and other scavengers are a non-issue as long as you keep all of the sweet smells a long ways away from your bed, this includes food, tooth paste, deodorant, gum, anything with a smell–doesn't matter if it's packaged or freeze dried, bears and Candis can smell through packages and bags–if it has a smell, put it in a cache. If there's nothing but you and your stinky human stench in your sleeping bag, then you can be pretty confident that all the big critters in your vicinity will leave you alone.
The smaller critters... well, pack rats will make off with your keys and eat a hole in the foot of your expensive sleeping bag so they can get fluff for their beds. If you're at a backcountry campground that has ropes in the trees, it's to hang your gear off the ground so nothing gets stolen by the local wildlife. Last camp I went on with a big group, we carried an extra tent just to store all of our gear in at night, but there were also people there sleeping under tarps. I think it really boils down to whatever you're more comfortable with. Myself, I'm ok with carrying the extra weight so I can have the extra comfort at night, keeps my gear cleaner too.
As far as risks, I don't think there are any more risks using a tarp than there are using a tent. You put yourself more at risk to exposure than you do to wildlife. But if it's something you're going to worry about, then you might just get a better nights sleep in a tent where you're not going to be up all night paranoid that something's going to slither up to your face in the middle of the night.