Unconventional Learning Experience

The show you're watching is not made for educational purposes, nor is it a total Aesop magnet. It most certainly isn't full of And Knowing Is Half the Battle sequences at the end of each episode. But in spite of all that, you start inspecting the series in depth and in full detail and come to the conclusion that it's most definitely not the negative influence that the critics and folks keep on claiming it to be. Thanks to the various wikis and fansites that show up all over the internet, this trope has grown more and more persistent, to a point where small bits of Genius Bonus are uncovered. Keep in mind that series that invoke this do have their fair share of Aesops, but the educational value probably isn't going to come from them.

Compare and contrast I Read It for the Articles.

Newspaper Comics

 * The Far Side

Comic Books

 * Peter David tells a story from back when he was still writing The Hulk of how his daughter's second grade school teacher once sent him a note informing him that if he kept allowing her to read comic books, her vocabulary would be sub-par and her reading level stunted. So David pulled out three or four issues of The Hulk he had on hand and started writing down some of the notable words used in the dialogue and narration. Words like "sepulcher" and "cravenly" and "unconsolable" and "cylindrical". He then asked if it was usual for a second grader to not only read such words, but to know their definitions. He then closed his case.

Live Action TV

 * NCIS is definitively not educational, but between all the movie references that Di Nozzo brings up from nowhere and how he gets weird plans from them (and Abby, of course), people can learn a lot about movie classics just by watching the series.
 * Myth Busters is in the business of busting myths, so it is educational, but notably, several people have credited the "what to do when your car is submerged" episode with saving their lives.
 * The Wire demonstrated, in one episode, that gambling can be used to teach probability math.
 * In fact, if The Drunkard's Walk is to be believed, gambling is probably the only reason probability math was invented.
 * It also offers some excellent advice on how to avoid electronic surveillance and self-incrimination when you get arrested. Police departments complained about this.
 * Instead of watching 24-hour news networks, you can tune in to The Daily Show and The Colbert Report which satirizes these programs, and still get a good chunk of pertinent information on whatever it is they report.
 * In the case of The Daily Show, It's got to the point where some people use the show as their main source of news. Jon Stewart is uncomfortable about this, since he sees his show as a satire and not a straight-up news program.
 * You can learn a great deal about historical artifacts from Pawn Stars and it can even show you how to avoid damaging valuable antiques.
 * Numb3rs discusses math in every episode.

Tabletop Game

 * Dungeons and Dragons can easily be considered as a long arithmetic problem that is oddly enough personified as a fantasy adventure.
 * Tabletop RPG games in general can be classed as such as well.
 * Arithmetic is particularly taught by any Tabletop RPG that features a Point Build System, Min-Maxing or both; any system that uses a form of combat resolution that isn't narrative (i.e. that uses dice, cards, etc) teaches probability theory; and, if you play them long enough, every single Tabletop RPG in existence teaches Game Theory (though intuitively rather than formally).
 * One of the side effects of being a fan of the Hero System is your algebraic abilities get a lot of workout.
 * Board Games and Card Games also teach probability and, in some cases (looking at you Monopoly and family), arithmetic.
 * Even Plugged In admitted that the Yu-Gi-Oh! TCG had the educational benefit of helping kids practice math.
 * There have been many cases in which parents reported that the Pokémon TCG taught their children basic math skills.
 * Some of the real world settings in the GURPS line are described in sourcebooks with a level of detail and accuracy comparable to that of a high school history textbook. Moreover, they're also good at explicitly separating myth and history.

Theater

 * Assassins
 * 1776

Video Games

 * The Assassin's Creed series fit this nicely. While a lot of it is fictional, the people and places (besides the protaganists) are very very real.
 * Except nearly every single non-fictional character is a case of Did Not Do the Research. Acknowledged and handwaved within the series by saying the Templars wrote the history books. And speaking of the Tamplar…
 * Both Age of Empires and Civilization can arguably count as a more interesting way of learning about history and technological developments. Civilization in particular is notable for its Civilopedia, from which you can learn a great deal.
 * Additionally, Sid Meier's Alpha Centauri, the Spiritual Successor to Civiliation, gives you just enough info about fields ranging from ecology to economics to sociology to philosophy to Chinese poetry to make you want to look stuff up when you are inevitably forced to quit, as well as including some pretty cool projections about plausible near-to-middle future (next 100-500 years) technology. At the very least, it will completely disabuse you of the notion that genes are blueprints…
 * You can learn a lot about China's Three Kingdoms Period from Dynasty Warriors, and a lot about the Sengoku Era of Japan from Samurai Warriors… just as long as you remember to take it all with a grain of salt. If nothing else, you might get interested enough to look some of the characters up, just to see how much they were changed - and better yet, how much of the awesome, far-out stuff was actually REAL!
 * Dwarf Fortress. How to make steel, properties & types of different rocks, the use of potash in farming techniques, the true meaning of the serenity prayer…
 * Medal of Honor and other First Person Shooters set in World War II can teach younger players about the time period... along with a few bits of questionable accuracy and a heavy dose of America Wins the War.
 * Pokémon teaches you math. If your normal-type mon just used a base power 30 water-type attack on a foe Venusaur chopping 1/6 of its health, and you have another mon that outspeeds Venusaur but can be two-hit-KOed by it, and that mon is a fire-type with about the same special attack stat as your first mon and has a base power 30 fire-type attack, should you switch it in? (Answer: )
 * Don't forget the 2nd Generation games, which taught you Visual Braille!
 * Sid Meier's Pirates! certainly taught a lot of people the geography of the Caribbean.
 * According to TIME magazine, Steven Johnson argues that Sim City taught his nephew about taxation issues, and that even a segment of one The Legend of Zelda game had enough detail to "bury the canard" that it is passive entertainment.
 * There are many gamers out there that claim RPGs taught them how to read, or helped learn a second language.
 * One fairly high-up Facebook employee wrote an essay detailing how much of his current business expertise had its inception while trying to master Starcraft.
 * Extra Credits had an episode on "tangential learning", which was on the very topic of how video games, rather than being the brain-rotting evil incarnate the Moral Guardians claimed, was in fact an easy way to learn various facts about many things depending on the plot in question. It didn't even need to be exact or in-depth to work, as, for example, God of War, despite its inconsistencies with actual Greek Mythology, could encourage someone to go and read about it, or Mass Effect could encourage someone to go and read a book about Dark Matter or the Galactic Core.
 * The Total War series can teach a gamer quite a lot about the different periods of history, despite various inaccuracies. Some mods like Europa Barbarorum (for Rome: Total War) have been created with the help of university professors and the like, thus going so far as to teach the audience about economics, politics and even languages of the ancient world.
 * Shin Megami Tensei for some gamers, taught them about Religion (from Christianity to Hinduism) and Mythology. The Persona spin-off series (especially from 3 onwards) also covers a wide range of topics from geography to advanced english language to the major arcana and of course, Jungian psychology.

Western Animation

 * Things that can be learned from Avatar: The Last Airbender:
 * Eastern Philosophy/Metaphysics
 * Traditional Chinese Characters
 * A total solar eclipse lasts around 8 minutes.
 * Western elements and cosmology.
 * at least most of the chakras were accurate, at least in name
 * There was a story of a boy who saved his friend from choking by using the Heimlich Maneuver, which he learned from The Simpsons.

Other

 * Porn, if you're learning to draw anatomy. Not if you're trying to learn sex.
 * Watching/reading works in foreign languages