This book is full of wonderful characters, and listing all of them and their personalities is a large task; therefore, I am going to limit this answer by focusing more on the main characters of the text.
First up is Mole. Mole is a wonderful character, and he's quite dynamic as a character as well. He's an underground species of animal, and heading out into the wide-open, above-ground world is a brave thing. Mole is brave in this regard, but he's also somewhat timid and reserved when the story begins. By the story's end, Mole is a much braver and self-reliant character. One thing that never changes about him is his loyalty to his friends.
Next is Rat. He is Mole's best friend. If Rat was a person, we would call him a gentleman through and through. He's kind, sociable, patient, and he accommodates the needs of his friends. He is also well-mannered and not someone that is going to shirk out on his duties.
Toad is imprudent and impulsive. He's very much a quintessential rich playboy. He believes that things exist to be used by him in order to make his life more fun. He isn't my idea of a good time, but he is full of boundless energy that simply refuses to be contained. He is gregarious and loves to be the center of attention, and he uses his money to achieve that end.
Badger is wise and dependable. He's very knowledgeable about the Wild Wood, and he has the great ability to get along with basically everybody. He's not quick to jump into conflicts of any kind, but he is usually aware of a conflict. Because of his intelligence, wisdom, and ability to know about the conflicts, he is a dependable source of resolution to conflicts. A good example of this is when Badger uses his knowledge of the secret underground passage that he uses in the battle to regain Toad's home.