You probably refer to the so-called 'banned cartoons' you find a lot on YouTube these days.
The truth is, none of these cartoons were 'banned' as such by any one government or institution.
At the most they were taken out of circulation, withheld or ignored from broadcasting by the very companies that had produced them. They have been and are however available in various forms and medias.
The reasons are often because the cartoons in question contained subjects, characters, scenes and circumstances that by contemporary standards are perceived as offensive. The main reason however is often for containing racist themes or stereotypes.
During the World War II period several studios such as Warner Bros. and Disney turned out cartoons in support of the war effort. Undoubtedly they had anti-German and anti-Japanese overtones, often very strong ones.
Donald Saluting Hitler
Germans -- and in particular Hitler -- were depicted in very broad stereotypes as alternately dumb, abusive, ugly and ignorant. Asian stereotypes were even worse off, undoubtedly contributing to American Xenophobia at the time.
While appaling to modern audiences, these stereotypes were not just accepted but also expected. Being at war with Germany and Japan meant that any parody or disregard towards these nations was patriotic.
Examples of such extreme stereotypes are
- 1943 Daffy -- The Commando
- 1942 The Ducktators
- 1943 Donald Duck -- Der Fuhrer's Face
At about the same time racism towards the black community in the US was still very strong and the depiction of black stereotypes was rampant. It was completely normal for studios to create cartoons with racist undertones or at least stereotypical elements that are nowadays perceived as offensive.
An interesting example would be the so called "Censored Eleven" cartoons, a group of Looney Tunes and Merrie Melodies shorts. While probably not intended as hateful jabs at the black community (such as the jabs at the war enemies) they did depict characters with either exaggerated black features or personalities, accents and behaviors.
Even today we still see companies pull their own products for various reasons, with varying results.
Ren and Stimpy for example were discontinued for their depiction of extreme exaggerated violence. Speedy Gonzales was pulled for being a perceived ethnic stereotypes, albeit Warner Bros. received a backlash from the Hispanic-American community since has was not seen as offensive, but actually as a cultural icon.