He loses and falls victim to the cockroaches in many episodes, but in some other episodes he reigns victorious as he defeats them.

Oggy holds an intense grudge against Dee Dee, Marky, and Joey, which was created even when he was a baby (revealed in the episode 'It's a Small World'). In the episode 'Don't Rock The Cradle', she has a baby and wants Oggy to babysit the baby. Occasionally, however, Oggy has to stop Jack when something is going wrong to Jack. Also, Jack is often there to save Oggy from the evil plots arranged by the cockroaches.

Sometimes Oggy wins over the cockroaches with help from Jack. Jack is Oggy's cousin, even though Jack is crazy, he is still a friend to Oggy. She was Oggy's mate, but their relationship is already broken-up because Oggy wears wrong clothes to come her house. He became jealous when Marky came to her. The former friend who appreared in two episodes ( Jealousy and The Joker Joked).

The new mate the next door neighbor, he fell in love with Olivia, in the episode ' Olivia', he saved Olivia's life, making Jack and Bob jealous of him. Oggy has come to realize that without the cockroaches, nothing fun or interesting ever happens in his life. In one episode (So Lonely), he even uses a tape recorder with their laughter on it and plays their pranks on himself out of boredom. Whenever he finds himself alone in his house, he will eventually begin to miss the cockroaches along with their pranks. It was revealed in the episode 'The Outsider', Oggy was terribly afraid of mice. Despite the constant mayhem caused by the cockroaches, Oggy has developed a sort of love-hate relationship with them, having lived with them for a long time. Although sometimes acting somewhat female (or in some cases, dressing like a maid, gardening), or male (in one episode the roaches steal his laundry bag and keep dropping a track of clothes - Oggy picks them up one-by-one, but, embarrassed, moves off screen when a brassiere becomes visible among the boxer shorts and socks). Oggy usually spends his time either watching TV or doing housework - when not chasing roaches. Oggy has a blue body, a red nose, a pink tongue, a grey tummy, whiskers on a yellow circle, pointy ears, and gloves.

Oggy the cat