Eventually, new anime fans will notice that a series they're watching has borrowed or directly parodied another program. Nods toward series viewers are familiar with can enhance an experience, and when someone sees that an anime they love is referencing a show they're not familiar with, it can open the door to a new series they might appreciate.
Anime like Gintama, Pop Team Epic, and Osomatsu-san contain countless anime parodies, but they also appear in slightly more unexpected places, like Food Wars! Some are blatantly obvious, like when Ichiko transforms into the great detective L, but others are a little more subtle, like when Saburo from Sgt. Frog walks into the room like he's Kaworu from Neon Genesis Evangelion.
Death Note is one of the most memorable and influential anime of the 21st century, so it's no surprise it's been parodied by other series. WataMote is a prime example of this. This anime is about a socially anxious teenager who will try anything to be popular, often with disastrous or hilarious results. In one scene, she researches ways to look more feminine and attract more boys, and it's animated as if she's Light Yagami on a supernatural killing spree.
Considering the low success rate of her attempts, it's oddly appropriate.
If an anime exists, Gintama has probably parodied it. One of the most memorable examples involves a shot-for-shot recreation of one of Neon Genesis Evangelion's most notorious conclusions. The ending in question shows Shinji standing in a circle while everyone in his life claps for him because he's regained some confidence.
Shinpachi takes Shinji's place, and he's applauded for realizing that his obsession with an idol named Otsu is more than enough to sustain him, and he doesn't need to be a samurai. This is only marginally less absurd than the original scene.
Nearly every scene in Pop Team Epic references some form of Japanese pop culture, which often means anime. In the first episode alone, there's a scene where Pipimi becomes a blurred out Totoro who is warning Popuko not to steal an umbrella, and then both of them get hit by a city bus. There's also a scene where the two characters stand in a beautiful landscape reminiscent of Your Name, while a song that sounds a lot like the movie's theme, "Zenzenzense," plays in the background.
What follows are a bunch of explosions, because this is Pop Team Epic and it's not supposed to be heartfelt.
If the main character walking around in One Piece cosplay wasn't enough of a parody, Good Luck Girl! includes some extremely direct scenes, including one Death Note parody where Ichiko contemplates her next move against Momiji.
Her face is literally replaced with L's hollow-eyed visage, and she sits perched on a chair with her finger in her mouth.