Yes. Absolutely. I'm not sure if you are talking about cartoons like these as we find them in newspapers or things like superman. Either way they are very useful and give us a quick and relatively easy to digest slice of public opinion. The cartoon maker wants the image that he creates to be easy to understand. He wants something that people can look at, digest quickly, agree with and then move on. In the above example it seems quite clear, even if you knew nothing about Hitler, that he is supported by two men, von Papen and Hindenburg. If either one of them goes away then Hitler falls. This is despite the Nazi party in the background, the two walk alone, carrying Hitler, indicating that despite Hitler's popularity and the party machine behind him that the two of them can make or break him. Similar can be done with older cartoons up to the present day. They are an invaluable source for the historian.
As for more conventional superman type things you could say that they tell us about the social attitudes of the time. What is an archetypal hero meant to be like? How does he, as the ideal man, treat women for instance? What is a villain like? A Soviet agent? Gangster? Does he have any obvious racial characteristics? For instance, if he had a big nose and side locks you could draw the conclusion that the artist and the audience don't think very highly of Jews. In that view cartoons might be very useful to a social historian looking for evidence of social attitudes and practices.
Oh, heck yeah!
First, it should be stated that just about anything has value as a historical source, but works of expressive art are always rich in historical information if you know what to look for.
The first thing you want to do is identify the creator, or group of creators responsible for the work and the audience, or the group that is intended to consume the work. As a historical source cartoons can tell you both what the creator wanted to say and what the audience wanted to hear. As works of popular culture, cartoons are often very receptive to the audience.
Let's take Private Snafu as an easy example. The Private Snafu cartoons were commissioned by the U.S. Army as training and orientation films during WWII and produced by legendary director Frank Capra. They featured many of the best known names of the Golden Age of animation, such as Tex Avery and Chuck Jones and included Theodore Geisel (later Dr. Seuss) among their writers. As training films, they largely focused on negative examples of Snafu failing to follow army protocol in regards to malaria prevention. As traditional cartoon morality plays, they warn against waste, laziness and ignorance, often at the cost of Snafu's life. These qualities tell us what the U.S. Army wanted to say with the Snafu cartoons, and therefore inform us of the internal problems that the Army felt it needed to address.
The audience is another interesting quality of the Snafu cartoons. The original motivation for the Army behind making a training cartoon was that it could target the less literate recruits. As it was made exclusively for military consumption, the creators could assume that the entire audience was young, male, American and mostly likely Christian. The Snafu cartoons are tailored for this audience, being slightly more bawdy than the very visually similar Warner Brothers fare, which can be surreal to modern viewers. They feature heavy use of pinup girls and Christian imagery and every effort was made to make Snafu reflect the typical soldier, down to his working class Brooklyn accent. Towards the end of the Snafu cartoons, after Germany's surrender, Snafu becomes increasingly competent and diligent, reflecting the soldier's own growing confidence in victory. These qualities not only make Snafu an interesting reflection of its audience, but also show what the form of cartoons in the Golden Age might look like when narrowly targeted.
So not only does Snafu tell us about the people that made it, some of the most famous names in animation, but also the people that watched it, one of the most studied groups in popular history. Snafu is kind of an easy example because of its ties to a major historical event, but any cartoon can be effectively analyzed as a historical source if you try hard enough.
Source: Private Snafu: What can a Cartoon tell us about the U.S. Military in WWII
Further reading: Animating Culture by Eric Smodin (Smodin, Eric. Animating Culture: Hollywood Cartoons from the Sound Era . New Brunswick, New Jersey: Rutgers University Press, 1993.)
Indeed, looking at any form of entertainment will give you an idea of what was happening when it was made. While most of the examples in the thread are american, looking at those made in other countries can tell you a lot about their cultures and political environments.
Propaganda cartoons were everywhere, particularly during WWII. There were quite a few cartoons made under nazi germany as Hitler was a huge Disney fan, the most well known of these were Der Storenfried, and Einigkeit Macht Stark. Japan famously had Momotaro's Sea Eagles which featured cartoon animals bombing an evil oni island base (the americans at pearl harbor).
Speaking of demonizing the americans, north korea has a slew of cartoons about defending Korea from the evil american ways. They are a sight to behold. A few years ago, one of these famously made rounds on the internet which depicts the americans as evil wolves that pilot cgi robotic jet crows.
I've also talked about soviet animation before, but it really is an interesting subject. Unlike many other forms of media at the time, animation was allowed a certain degree of creative freedom in regards to what it could show. If you are interested in the subject, I recommend checking out this dailymotion channel which uploads subtitled russian cartoons.
Absolutely. A useful, if rather mechanical approach is to follow this scheme: Find Out Before As Clues Are Hidden Figures, Objects, Background, Actions, Captions (or speech), Author, Historical context. By the time one has carried out this brief process one should be able to say what the cartoon is of, what is happening and where, what is being said, who designed it and when it was used. This one, for example, is really useful on Britain's stance on the partition of Ireland https://www.schoolhistory.co.uk/forum/uploads/monthly_03_2007/post-5215-1175202511.jpg
