Yup, I ride mostly rural areas at night, so deer and other critters are my main concerns. Even more than the occasional jerk driver.
Although the only animals I've hit while riding a bike are dogs -- and somehow I managed to run over them without falling. The last was a neighbor's big goofy pit bull, a harmless big lug who thought I needed a dog parade and stopped suddenly in front of me. But still could have been painful if I'd fallen. I ran over the dog's haunches, which, for a pit bull, is like a gentle massage. It was fine. I was fine. Not something I'd care to risk again.
Little critters can cause crashes too. A friend fell over a little armadillo that darted into our path while riding home one night a few years ago. Fortunately he fell on the grassy roadside, just some scrapes and bruises. Could have been a lot worse. I've had many close calls with skunks, raccoons, possums, cats, rabbits, even owls and hawks. And a few snakes. Usually I stop for snakes and chase them off the road. The funniest was a toddler skunk that waddled toward me from the pasture, while mama was desperately trying to herd her young'un back to safety. Skunks are hilarious, too friendly for their own good. We rescued a couple years ago when we lived in a rural area, nursed them back to health and released them. They can become domesticated very quickly. So far I've never been sprayed by one.
And a relative was badly injured several years ago when she hit a deer -- it slid up the hood and the antlers jabbed her face. She needed a lot of reconstructive surgery. I can see why some folks prefer those massive trucks and SUVs with squared off hoods. Bad for pedestrians and cyclists, due to the compromised sightline. But safer for the drivers and passengers.
On night rides I usually mount two or more single LED headlights. I'll run two at a time, and switch to the third or fourth after the batteries run down on longer rides.
One of my best purchases last year was a NiteRider Lumina Dual 1800. Two LEDs side by side, lens designed to produce an even, shaped beam comparable to a motorcycle headlight, slight overhanging hood to minimize spill into eyes of oncoming drivers, cyclists or pedestrians. The beam is wide enough I can usually spot the glow of critter eyes along the roadsides.
And it'll run 3 hours on medium, 700 lumens, plenty for most situations. On longer rides I'll carry a spare small NiteRider as a backup, since it fits the same quick release mount.
I also use low power lights on my helmet. Not bright enough to really light up where I look, but does catch the reflective eyes of critters grazing or lurking along the roadsides.