How about one of these...
Hanna-Barbera produced
Scooby Doo; Tom and Jerry; Pixie and Dixie; Top Cat; Huckleberry Hound; Yogi Bear; Snagglepuss - "Heavens to Mergatroyd"; Wally Gator; The Addams Family; The Flintstones; The Jetsons; Secret Squirrel; Wacky Races starring Dick Dastardly and Muttley; Help! It's The Hair Bear Bunch; Hong Kong Phooey; The Smurfs; Jonny Quest; Dexter's Laboratory; Cow and Chicken; Johnny Bravo; The Powerpuff Girls...

Then there's Disney, Warner Brothers, MGM, Pixar, Fox, Dreamworks and all the Japanese manga (including Pokemon and Digimon).

Peanuts with Charlie Brown inspired Jed and Jamie's favourite: Bill Waterson's Calvin and Hobbes (aka 'Tommy og Tigern' in Norway) - shown below and left (mouse over the left hand one for the next frame in the cartoon). Many of the old black and white comic strips are crying out to be traced in Illustrator and colour added.

Extending the brief:

Cartoon characters are often used on packaging and instruction leaflets. You might develop your cartoon project into something substantial which integrates with text and logotypes, perhaps in conjunction with a program such as Photoshop, InDesign or QuarkXPress.

The pasta shapes tin on the left combines the main characters with the HP logo, many pairs of eyes and stylised pasta shapes, arranged on an orange and green split background. All may have been done in Illustrator, except for the Scooby-Doo! logo's soft glow which has probably been done in Photoshop.