We're running a fantasy game where the adventurers frequently travel through the wilderness. Too many of the threatening encounters they have are with fantasy creatures (like goblins, orcs, etc.). What kinds of non-fantasy creatures could pose a threat to them?
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Lions and Tigers and Bears... Oh my!
I think the number of dangerous creatures out in the wilderness is almost innumerable, so I will just list categories with a few examples.
I have torn more than one group of adventurers to shreds with wolves. Wolves are smart team-hunters. They harry and feint. They wear groups and individuals down. They work together and coordinate their attacks.
Make them spend a night or two being howled at all night. Make sure to use whatever rules your system has for fatigue. Don't neglect the fact that taking a watch means you're short on sleep.
The group stays together huddled around the campfire? Then they don't know where the wolves really are. They send out scouts and outriders? The wolves take those poor lonesome souls down.
Boars are hard to beat for daylight attackers. A boar rushes the party while they're going single-file along the woodland trail? Disaster! A boar is an 250+ lb monster with huge tusks that can leave men and horses bleeding, crippled, or dying. It can charge like a bull, and even kill you after you've killed it - thus the stout crossbars through boar spears, meant to keep a boar from gutting you by running up the spear you just impaled it on!
Australian boars are known to be predators, too, so if you want man-eating boars, that's not much of a stretch.
I have made the danger of wilderness trekking clear to parties in several systems with both of these animals, with nary a green-skinned humanoid in sight!
Major threats include
Not creatures in the typical sense, but still:
Fear: A rumor about a creature, some weired noises and difficult terrain make some interesting nights.
Bacteria and Virus: A wound, an infection and no healer around .. try to find one.
People: The last time this village hat visitors from abroad, two babies died. Guess what your heros aren't welcome
Traitor: Maybe one of the travelers gets paid for doing harm or has to do it in order to see his son again.
Hunger and Thirst
Realistic Animal Attacks
In the US, there's plenty of data on what animals actually result in deaths. Bees/wasps and dogs are way in the lead, as well as "other specified animal" which is more accidents with horses and other agricultural animals (though that means you shouldn't omit the risks of the party's own beasts of burden). There are attacks and even deaths every once in a while from deer, moose, and captive chimps too, but these are exceptions and not really worth including in general, though the occasional demented usually-safe creature can add flavor.
In Africa, for example, hippos and cape buffalos, allegedly herbivores, have killed many more people than lions have. Wolves and big cats have some kills, but that's a bit more rare, and usually only when the animal is sick or something else is up.
And it depends all what you count - this article lists the top deadly animals in Africa, and mosquitoes are #1 and humans are #2... If just "passing by," animals like apes and bears really aren't usually a threat, but if the group stays in one place and becomes an issue in their territory they might.
You can have normal animals being more aggressive, like unprovoked wolf and lion attacks galore because they come up on a random table, but then they are really fantasy animals and not real animals.
In the water, you have sharks and jellyfish as the primary killers. Other things kill only very occasionally and usually when being messed with (such as the unfortunate death of the Crocodile Hunter to a stingray).
Here's two groups that might not immediately come to mind when you think of dangerous animals:
Insects
Swarms of angy wasps and bees, biting ants, disease carrying mosquitos, poisonous spiders... a lot of options there, and every single one of them can take down a human. Often very painfully. A cave enterance thats also the hive of aggressive wasps. Fire ants make the PCs sleep in make-shift hammocks in the trees, but the trees are crawling with poisonous spiders. Or a druid cove protected by millions of loyal bees.
Fish
Its an odd choice, I know. While the PCs are crossing a river, and looking out for aligators... well, there's plenty of fish out there that will happily tear into human flesh. Or worse, horse flesh, leaving the PCs without mounts.
I live in a rural, forest area. We have all manner of wildlife here that's dangerous when you mess with them.
However, most animals aren't really aggressive. Sure, they'll attack if cornered, or if they're hurt or rabid, but generally speaking, they'd prefer to avoid humans. Still, if encountered in the appropriate circumstances, there's wolves and coyotes and snakes and bears and insects and even deer and raccoons can be dangerous.
Now, if you want aggressive dangerous animals...
Bears aren't generally aggressive, at least, not the bears we have here. UNLESS they're mother bears protecting cubs, in which case, they will destroy you. Or if they've become acclimatized to humans. Nearly all the bear attacks that have happened in this area have been due to humans getting to close to baby and getting mauled, or bears associating humans with food through ill-advised feeding and dumpsters. They WILL not hesitate to eat you if you don't give them the food they think you have.
Wild boars are just mean. Stupidly mean. Someone above said they were about 250 lbs, but the ones we have here are bigger than that. They're bigger than the bears. I have seen a wild boar leave dents in the bars of a cage made of inch thick steel stock. I have no idea why they're so aggressive, but they don't need a reason to try to murder you.
Something you might not have thought of, but are likely to have closer to towns or former towns are feral dogs. We had a pack of those here a few years ago; escaped from people's property or just abandoned. (In this area, dogs aren't usually leashed or penned.) They're not afraid of people, like the acclimatized bears. They can be worse, though, because while they're individually smaller, they form packs. Think of them like wolf packs that don't avoid people.
And if your party ventures anywhere near a lake or a river, swans, geese, and snapping turtles are all surprisingly awful. Swans and geese WILL attack aggressively, especially during nesting season. And snapping turtles, in addition to being ill-tempered, can bite through fingers and other extremities.
Also, badgers. Forgot about badgers and their ilk. Like wolverines.
I give you the dreaded Aurochs
Aurochs were found throughout Eurasia until the 17th century. These were essentially wild cattle that were half again as big as modern cattle. They could stand close to 6 feet at the shoulder with horns spanning about 5 feet, and weighing up to 3500 lbs. An encounter with an ill-tempered bull aurochs would certainly ruin your picnic.
If you want to include animals, give them the home-ground advantage.
There was an old saying that "the most dangerous animal in the forest walks on two feet" ~ it is a reference to mankind.
Your setting, being more or less a temperate Eurasian analogue, is nicely suited for the greatest danger to the characters (potentially) being other humans that the party encounters. Bandits / brigands / outlaws, fanatics (like the White Cloaks of Robert Jordan's Wheel of Time), mercenaries guarding a caravan who assume the party to be a small band of brigands or bandits, cattle rustlers who hold that "dead men tell no tales" and are armed, smugglers, various pastoral peoples guarding their sheep/cattle/horse herds' grazing areas, adventurers, assassins, deserters from an army, rangers protecting their lord's forest or livestock, outriders and scouts keeping the local duke's territory safe from wandering miscreants (which the PCs are assumed to be), servants of a magus or a cult leader seeking new victims to experiment upon or sacrifice (respectively), border guards with permissive rules of engagement and itchy trigger fingers - these are all potentially canny and dangerous opponents who are "the beast that walks on two feet." They are also encounters that may be resolved without resort to bloodshed. 1 This makes them quite flexible as a tool for the GM. (A substantial portion of the encounters I ran when I GM'd Empire of the Petal Throne ended up being other humans, encountered near or on the Sakbe roads, although plenty of more monstrous encounters were to be had as well).
For an occasional Jurassic Park feel, you can introduce a lush valley where packs of small to medium sized dinosaurs roam about looking for a snack. Similarly there is the threat of soaring lizards such as pterodactyl flocks - that can pose another hazard from their nests in the hills / cliffs / mountains. (Substitute in giant eagles or rocs looking for fresh meat to feed their chicks and you've got most of the aerial hazards covered but those are more 'fantasy' than not).
A character getting sick doesn't usually make for a great adventure, unless you can morph that threat into a "Arglbargl is sick, we must find a cure" which leads to other encounters where someone has to "cut the heart out of a yak and boil it in a snow panther's gall for an hour before you feed it to Arglbargl" as a cure. This would necessitate meeting a local shaman/healer/wise woman who offers that cure as the only way to save them from the wasting disease.
A very memorable scene / vignette from the mini series Lonesome Dove included a river crossing where there was an infestation of cotton mouths / water moccasins posed a lethal threat to horses, cattle and men.
Now and again herd animals will stampede. Anyone and anything in their way is in peril. Use of terrain and / or use of their wits is how the party will evade/survive such an encounter (or possibly perish if a TPK is a potential for your table).
Hungry wolf packs or hyena pack who outnumber the party can pose a threat to them.
This is something of a RL hazard near to where we now live, and other places where we have lived; wild boars, javelinas, and feral hogs all have a mean streak that can trigger when disturbed or threatened. They are also cunning and smart, as animals go.
Every so often Army Ants swarm forth and plagues of locusts ravage the land. Characters caught in such an event must deal with it or potentially perish.
1 As but one example for one game, the AD&D 1e Monster Manual had listed under the variety of "Men" the following kinds: buccaneer, berserker, pilgrims, dervish/nomad, merchant, caveman, tribesman, bandits and brigands
Its not animals you have to worry about, its nature. Jens answers are spot on. Its not exciting, but its fact.
One of my players is a wildlife biologist, and he said "i want to run a one-shot where your citified characters have to track overland and do an outdoors adventure". MISTAKE! Yes, there were creepy insects, angry druids, sacred spirits upset at us, but by and large it was the fatigue, disease, hunger, thirst, and terror of what COULD happen. Yea, a large cat terrified our horses at night and we lost a few. More predators beyond the firelight cause tamed animals to scatter. Supplies run low, terrain is brutal, horses come up lame and pretty soon no one has any solid sleep because everything IS out to get you outdoors. Ants, snakes, spiders, and all manner of 100% natural hideousness assaulted us.
Character lose weight, and temporarily have their CON, health, whatever reduced. Reduced resilience, decreased speed, strength, etc. made the few encounters we did have that were easier stand up fights into moments of terror.
I think it's important to think firstly, what is the campaign about and how to get immersed in the setting and role-play.
As a GM/DM when I'm working on the lore and history and myth of a campaign setting, I think about what is common and what is not.
I've adapted some questions to ask myself questions about creatures in a given campaign:
Some world settings have more of a particular creature type in them than others. Consider these redacted questions which often suggest the answers to other questions.
For instance, I've played in campaigns where a race was lost, (e.g. Elves) and they only figure in the tales of old - until they don't. So, it creates nice plot hooks. Elves were "fantasy" in the actual campaign setting as opposed to thinkiing what is fantasy to us as human beings living in the 21st century.
Many people I know would think that a creature that can create a super-heated bubble beneath the ocean which is hotter than the surface of the sun would be utter fantasy and myth, yet that is exactly what the pistol shrimp does. My point is that it may be more helpful to think about the question in the context of your campaign and that only you as a GM/DM can determine that.
You mention goblins and orcs as fantasy, but I think to some extent that can bring the GM/DM and players out of role-playing. If the PCs know that the goblins and orcs are commonplace in your world setting, then they are not "fantasy".
You can also weave in common tales and things that appear dangerous but are not. For instance, there was a myth in a campaign I played in which red squirrels where uncommon (as in real life) and were an ill omen. Meeting one suggested that a terrible thing was about to happen. The GM/DM made us all roll dice for fear checks when we came across one or more red squirrels. In the world setting itself the red squirrel was terrifying! If we failed our check, we had to run away. Later ther was a storyline which led us to uncover the origins of these doom-ridden red squirrels, which was very fun. We knew as players the red squirrels were harmless... but in the campaign, it was a whole different story. The GM/DM was clever and he put dangers ahead that re-inforced the ill omen of the squirrel, e.g. we ran away, straight into a trap! This re-inforced the myth of course because: We blamed the red squirrel!
Otherwise, I suggest you use common Beasts as a non-fantasy threat, but enlarge them, e.g. a Giant Polecat could be a significant threat in a low-level campaign - let alone a group of them.
The other non-fantasy creatures which were dangersous in previous campaing settings have always been other commonplace Humanoids. They can provide another excellent non-fantasy threat.
Although this won't help you in a high fantasy campaign, I've used a small band of rabid wolves to scare the bejesus out of a party recently. There isn't any magical Cure Disease in our campaign, so getting rabies was a real concern.
