What wild animals are there in California that can be dangerous or create hassles, and how do I avoid problems with them?
American black bears
They are somewhat common in some wilderness areas of California, mostly in the mountains. In their natural state, black bears are thinly populated on the landscape because it takes a large area to support one, and they are also shy of humans. Black bears are not very large; females can be the size of a large dog. There are certain specific wilderness areas in California where there are denser populations of black bears that are habituated to humans and dependent on human food. Examples of such areas are Yosemite Valley and Little Yosemite. This type of bear can be aggressive. The best way to avoid hassles with them is to avoid camping in the specific over-used areas where they exist. For example, you can start a backpacking trip from Yosemite Valley but camp way out in the backcountry. In addition, you can carry your food in a bear-proof canister, which can be either bought, or rented in places like Yosemite Valley. Bear canisters are legally required in many areas of the Sierra.
The same areas with bear problems also tend to have lots of smaller animals that are also habituated to humans and accustomed to begging or stealing human food. These can include squirrels, chipmunks, and marmots. The same precautions that work for bears also work for these animals: keep your food secured.
California has not had grizzly bears for about 100 years, except on our flag.
There are no wolves in california
Coyotes are small, shy scavengers that are mainly a hazard to small housepets. If you're lucky enough to see one, it will probably be around dawn or dusk, and it will probably run away into the bushes, or perhaps watch you from a distance. If you have a small dog, don't let it run around off the leash at dawn or dusk in areas where you know there are coyotes. Ditto for very small children; there have been cases where coyotes have bothered toddlers, but your chances of having this problem are probably about the same as your chances of getting bitten by a shark.
Mountain lions are rare and can kill people, and I don't know of anything you can do about that risk. They sometimes stalk people for a long time without being deterred by yelling or rock throwing. They also sometimes spring out of hiding to attack hikers and mountain bikers.
Rattlesnakes are pretty common. They're not aggressive. The most common reason for bites is that the snake is sunning itself in the middle of a trail, and a hiker steps on it without realizing that it was there. It's possible to get aversion training for dogs so that they learn not to pick a fight with a rattlesnake.
Different parts of California have different wildlife, so you should probably narrow the region. Anyway, I'll talk about the areas I'm familiar with.
In the Santa Cruz mountains, there are a lot of pumas (mountain lions.) Encounters are very rare. The advice is that if you do encounter one, make yourself appear large and noisy by waving your hands and your hiking stick; if you are attacked, fight feriously, using sticks and rocks to try and injure the animal (an injured animal will run away). It is very possible for an adult human to successfully fight off a mountain lion - an adult mountain lion is roughly the size and weight of a large dog.
In the Santa Cruz mountains, there are no bears.
In the Sierra Nevadas, there are a lot of black bears, particularly in the Yosemite area. Black bears are very mild, docile creatures. Normally they want to avoid encounters with people. When encounters do happen, it's usually because they want your food. Again, the same advice applies: yell at them, wave your arms - don't not run (running away triggers the predator instinct). Nor should you attack, of course. But if you are attacked, fight ferociously and try to injure the beast.
I've gone on two 3-day backpacking trips into the Sierra backcountry, and did not see any bears at all. One of the trips was only about 10 miles north of the Yosemite area.
My coworker last year spent 30-days on the Pacific Crest Trail, hiking from Washington State into California, hiking along the Cascades and the Sierras, and he never saw a single bear.
Other large, potentially dangerous animals don't exist in California. Back in the old days, there were wolverines, wolves and grizzlies, but those were pushed out 80 to 100 years ago.
EDIT: ... Interestingly, my wife and I are some of the only people in California to actually hear the only wolf that has been living in the wild in California in the past 100 years. We were camping in the Cascade mountains in Northern California a couple years ago, and heard wolf "OR-7" howling.