Ayakashi Ayashi is pretty unsubtle about telling people to stop daydreaming and focus exclusively on real life. It's about giant monsters coming to life when someone is dissatisfied with living in a Crapsack World.
To sum up, the writers of Blassreiter would like you to know that anyone who is mean to immigrants is pure evil, the media is full of idiot sensationalists, and if God is there He does not like you.
Fairy Tail: The series is infamous for laying the "friendship solves everything" moral rather thick. While The Power of Friendship is common amongst shonen, Fairy Tail in particular earns scorn for frequently preaching its importance and rarely teaching anything else.
Being about how war affects humanity, the Gundam franchise has dropped many anvils over the years.
The original Mobile Suit Gundam, including its subsequent sequels had a minor subversion by dropping opposing anvils at the same time.
Much of the protagonists' angst in Gundam SEED comes from the fact that they have to fight each other for reasons they don't know. Then the second half of the series comes and practically every second sentence that comes out of Lacus' mouth is relentless bashing of the Cycle of Revenge. Then SEED Destiny comes along and drops the same anvil all over again, along with a second anvil bashing Shinn's views of the world.
Another repeated message from 00 is that the only way to peace is through understanding others. It is repeated twice in the film's postcredits scene.
Also, a quote from the leader of the Union...
"They're aggressively ending conflict all over the world. Isn't that our job?"
As said above, Gundam has dropped many anvils over its span. However, there is one common anvil that transcends each series: "If we all understand each other, we can all stop fighting, get along and be happy." This theme has existed since the first series (as it was the basis of Zeon Daikun's Newtype theory) and has been carried over the rest of UC (all the way to Gundam Unicorn) and even further into the AUs; among the latter, only G Gundam subverts the message due to its kung fu action movie themenote which essentially claims understanding can only be achieved through fighting. Alongside, said message is usually presented as the basis of the resident universe's telepaths and their purpose; this is especially the case with the Innovators of Gundam 00note in which Setsuna's ultimate attack is causing spontaneously generated telepathy among those in range so that automatic understanding can be achieved and the X-Rounders of Gundam AGEnote which was the whole reason Kio went through the Vagan Magical Mystery Tour arc.
In The Familiar of Zero, the episode in which Mr. Colbert dies was a very thinly veiled message about why war is bad, the entire second season being about how War Is Hell.
In an episode of the Kirby of the Stars, Dedede gets addicted to snacks and becomes grossly fat, unable to even stand up. This is followed by two characters announcing out loud that this is what happens if you only eat snacks and stay up all night watching television and Dedede being paraded through the town, pointed and laughed at. All of this before the episode is even halfway through.
Life keeps no subtlety in any of its themes. The whole manga is about a girl who is bullied, and the bullies themselves are two-faced Jerkasses.
The author of Naruto can't seem to be subtle about the whole "REVENGE IS BAD" thing, to the point that, until he kick-started the big war event, it took over the story. To make it worse, he seems to have equated revenge with a fully-justified desire to see someone punished for their crimes.
Be loyal to your village no matter what you do because it means becoming a sociopathic monster and trying to have ambitions other than the welfare of the village is evil and must be punished.
Which is turned into a Broken Aesop, as Shikamaru was portrayed as perfectly justified in seeking revenge against Hidan and Kakuzu. Even if you try to find some explanation for this, the fact that revenge is portrayed bad only for when the target is an Uchiha means such anvilicous aesop is already broken anyway.
By leaving someone in a state of continuous torture, until death... Convenient...
By planning to go missing-nin, which only didn't happen because Kakashi spoke up for him and his teammates. And it would have resulted in the deaths of Chouji, Ino, and Kakashi against Kakuzu had Naruto not conveniently shown up with his new Dangerous Forbidden Technique.
The Aesoptinum factor of Str.A.In.: Strategic Armored Infantry is made particularly obvious when not only is the research conducted on harmless aliens, but they look and act like little girls and anesthetic doesn't work on them. So every time one is dissected, they're being brutally tortured and the scientists just shrug and figure 'Hey, they'll get used to it eventually.'
You don't have to be watching Yu-Gi-Oh! long to figure out that the main theme is friendship. Not only do many of the main characters constantly make speeches about it (with Anzu/Tea being infamous for it, although there are many characters who are just as bad, if not worse), but there are also numerous motifs and symbols throughout the series which are meant to represent friendship. These include Yugi's Millennium Puzzle, the smiley face drawn on the hands of the main cast, and several different Duel Monsters cards. On top of that, the first syllables in Yugi's and Joey's/Jounouchi's names are purposely meant to spell out the word "Yujo", which means "friendship" in Japanese.