Let’s leave domestic dogs and cats out of this, because that’s too easy and dull.
So, what’ll it be? Rabid raccoon? Pack of wolves? Escaped lab monkey?
Turkeys. Or possibly Canada Geese. Probably turkeys though, the damn fearless bastards.
Western Diamondback Rattlesnake. 
Cougar.
There are coyotes nearby, including one that sometimes trots across our yard on its way to hide beneath the neighbor’s deck. It’s mangy. I’m afraid of it.
Moose. If I came across a mama and babies, oh yeah. But moose in general. I’m in danger in the car!
Stay away from the bars.
Canadian geese. They are not polite.
A man in our neighborhood was attacked by a raccoon the other week, so I’m going to go with raccoon. I occasionally see coyotes in open space/parkway, but they shy from people, so I’m not worried about them.
This is probably it for me as well, although it could be an elk or a mule deer. Not that an elk or mule deer is likely to attack (and we do have mountain lions and bears in the nearby mountains) but the snakes and ungulates are far more common.
Who would have known right? Figgin’ turkeys.
I have been attacked by Canadian Geese. I’ve been attacked (in my car) by a whitetail deer. I have been attacked by bumblebees. I have been attacked by a grey squirrel. I have been attacked by a bath towel. Once I was seriously threatened by a cricket. Oh yes, and I was attacked by a spider once - it pinned me to the floor. I’ve had wolves and foxes cross through my yard but they never offered to attack - by far the safest wild animals I’ve encountered.
Being in LA, it actually gives me joy that I could be attacked by a cougar, bear, or coyote, as well as obstreperous deer or unruly racoons.
But, to say most likely? Probably a cranky squirrel.
Attacked? Maybe a rabid fox or crazed deer. There may be snakes but I haven’t seen one in a long time and the ones I saw weren’t poisonous.
Do mosquitos count? 
Seriously, an escaped zoo critter might make it here if it ran through yards and jumped fences and such and stayed off the streets long enough not to get run over.
Rabid Fox. They may all be dead by now it’s been a while before I’ve seen any foxes, healthy, rabid, or mangy. A wild turkey is possible but they just seem to be passing through our yard so I’d have to hassle one to get him going. The coyotes have diminished, haven’t seen a racoon in forever, there are Fishers around but I haven’t seen one. Actually it’s pretty safe around here these days.
All of them. I live in Australia. Every damn animal here is deadly.
My biggest imminent threat of injury? My cat, who can go from purring with contentment to attack mode quicker than I can pull my hand away, and I’ve got very good reflexes. I know the OP said no domestic animals, but really he is the biggest threat.
I’ve also been bitten by a brushtail possum who used to sleep in my wine cellar before we had the house possum-proofed.
Bees and wasps can be a problem in Spring, and I’ve noticed the magpies are about to start their swooping season. They are nice birds for 11/12ths of the year, but utter bastards when their chicks arrive.
A squirrel nearly broke my boss’s leg.
Okay, she was jogging and was just trying to avoid stepping on it when it ran out from the underbrush, but still…
A really pissed off white tail deer i.e. Bambi.
I’m not too far from the King Fire (currently burning in California) and I’m a little worried about mountain lions and bears. They’re being burned out of their habitat and people are spotting them in unusual places.
We have a lot of snakes here too.
But in truth it probably will be a damn dog that gets me.
A raccoon if anything. Highly unlikely though.
Cockatiel or Indian Ringneck Parrot (they’re pets but under the law are exotic wildlife.) Otherwise, coyotes, black bears, or cooper’s hawks during nesting season. Cooper’s hawks actually built a nest near a government office a few years ago, then attacked the employees as they tried to go to work.