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. Whenever he finds himself alone in his house in Animville, he will eventually begin to miss the cockroaches along with their pranks (as seen in the episode, Priceless Roaches).
Oggy's house appears bigger on the inside, mainly featured in the roller coaster-like staircase scenes. Oggy has come to realize that without the cockroaches, nothing fun or interesting ever happens in his life.
Oggy is a diplomatic, sometimes lazy and an easy-natured cat who is the constant victim of the Cockroaches. Of all of his life, he spends his life chasing and catching the cockroaches, but somehow developed a certain love/hate relationship with them and also learn without the cockroaches, no fun will be invented in his life.
He also displays a love for gardening and eating food, which made him fat. Oggy seems to have a calm-demeanor but when provoked by the Cockroaches or someone, he would go and attack them. He sometimes do cross-dressing, because in one episode, the cockroaches steal his laundry bag and leaving trail of clothes and when he picks the clothes, he became embarrassed because there is a brassiere visible among the boxers and socks.
He is scared of mice, which means he is murophobic. This is ironic because real life cats aren't afraid of mice. In early episodes, Oggy, like his predecessor Tom, in Tom and Jerry, was the main punching bag in the series.
However, in more recent episodes, Oggy has been portrayed as heroic, often triumphing over the cockroaches despite the beatings he takes from them and Bob. Notable other accomplishments include winning the Formula 1, placing first in a marathon, and ultimately winning over his girlfriend Olivia.
Oggy is a sky blue cat with an overweight body, green eyes (sometimes black), a red nose which is removable, a pink tongue, a grey tummy, whiskers on a yellow circle, black pointy ears, and white feet.
In some episodes, his appearance is weak, but when he gets angry he is shown to be quite strong as he kicked Bob, Joey, Marky, Dee Dee and the robot cat counterpart of himself to the moon in the episode, Copy Cat.
- According to executive producer, Marc du Pontavice and France Info, the character was named after punk rock musician, Iggy Pop and the rock album, The Rise and Fall of Ziggy Stardust and the Spiders from Mars.
- The character had made several cameo appearances along with Joey, Marky and Dee Dee in most episodes from the animated series, Space Goofs.
- He is the only character from the series to have appeared in every episode.