Some canned goods might be allowed (always ask first) but perishable food is not. It can rot, smell terrible and grow mold. It can also attract rats and other rodents.
Pets and other Live Animals
This should go without saying, but you cannot have live animals in your storage unit. If you are going out of town, get a pet sitter or a friend to watch them.
Potted plants need sunlight, fresh air, water and new soil. Obviously, they will find none of that in a storage unit. Also, live plants can attract pests which can spread to other units.
You are not allowed to store flammable, corrosive, and explosive materials. These can cause serious damage to property, from your stuff to the facility buildings. Prohibited items include paints, paint thinners, pesticides, weed killers, fireworks, charcoal, liquor, and ammunition, among many others.
Stolen and Illegal Goods
Obviously, if the manager suspects you have stolen or illegal goods in your unit, they will have to call the police. This includes illicit drugs. You could be arrested and go to jail.
This is just a recommendation. In general, it is better to keep your valuables at home. However, any facility with good security, such as Peoples Storage, can be just as safe for your stuff.