You may be encountering problems with the king of urban pests, the city rat. You may also be having issues with its cousin, the gray squirrel, often referred to as the tree rat by disgruntled homeowners.
Former residents of the city, such as raccoons and opossums, may be encroaching onto your property (we actually encroached upon their property originally), as suburbs grow more crowded and they return to turn over your trash cans in search of food.
Your first thought doesn't need to be poison or another method of killing your fellow creatures. Even city rats can be admired in their own way, for their complete fearlessness and their ingenuity in getting food.
Still, even though you may not want to kill wild animals, you don't want to cuddle with them either. You just want them to live freely somewhere else.
There are various humane choices that can either deter wild animals or capture them so you can release them where they won't readily interact with humans.
The main deterrent is to block access to food, both inside and outside of your home. Steel trash containers with tight-fitting lids will frustrate even the most persistent animal.
Look for access points around your home and block them with 1/2" hardware cloth (wire mesh screen with 1/2" square holes). You can buy rolls of hardware cloth at your local home-improvement store.
You can also repel animals with essential oils. These are not the diluted body oils that you see in the mall kiosks, but pure essential oils, such as peppermint oil. Leave bits of oil-infused cloth around the problem exterior areas of your home (the smell is too strong for indoor use).
Capture and release
There are humane traps that you can use to trap problem animals and release them into an uninhabited area. They are essentially rectangular cages that allow the animal to enter the cage through a door that springs shut after they enter.
Some traps work by a mechanism that is tripped when the animal takes food bait that is placed to lure them inside. Others work with a spring-loaded mechanism that is activated by the animal's weight on a section of the floor of the trap.
These traps are available in various sizes for catching animals from rats to raccoons and foxes. Both raccoons and foxes can carry and transmit rabies, so releasing them requires great care to avoid being bitten. Both animals are normally nocturnal and shy, so if you see either animal wandering aimlessly in the daylight or appearing lethargic or disoriented, call animal control (or 911) immediately.
Unfortunately, the gray squirrel is very territorial, which is why you see them chasing each other constantly and why you will usually have only one squirrel that digs up your flower bulbs and causes other mayhem in your yard.
If you don't want to kill the squirrel, and it won't be repelled by oils or commercial repellents, you might consider offering enough nuts and seeds to keep it full and occupied and accepting it as your outdoor pet.
If all else fails, call a humane pest-control company like Beneficial Bats for help.