The Dexter's Laboratory episodes "Mock 5", "Trapped with a Vengeance", "Dee Dee's Room", "Game Over", "The Golden Diskette", "G.I.R.L. Squad"... there are a few. There was a episode where Dexter became an exchange student in Japan that poked fun at mecha, super sentai, and kaiju films. Then there are the Action Hank and Pony Puff Princess franchises, and the entire Justice Friends cast.
Duck Dodgers featured an episode that not only parodied Samurai Jack—Dodgers dreaming he's Samurai Quack—but the dream sequence itself was directed by SJ creator Genndy Tartakovsky and featured Mako as the voice of Quack's adversary Achoo.
Another episode featured an incredibly close to its source parody of Green Lantern, complete with Kilowog, Ch'p, Ganthet, Sinestro, and more.
The show itself is an affectionate parody of sci-fi has a whole, and the protagonist's name is a parody of Buck Rogers.
DuckTales had Gizmoduck, an affectionate parody of RoboCop. He was even named Roboduck in foreign dubs. Later became more like Superman when he appeared on the sister show Dark Wing Duck which itself was of course an affectionate parody of Batman.
Ever After High pokes fun at the awful parts of Fairy Tales while maintaining an upbeat and cheery attitude.
The Fairly OddParentsmovie, Channel Chasers, is all about this as Timmy, Cosmo, Wanda and Vicky go through various parodies of popular shows. It was finally lampshaded in The Simpsons parody with Timmy writing on the blackboard "This is the sincerest form of flattery."
Fairly OddParents also has the recurring character of Cat-Man, voiced by Adam West; an affectionate parody of his earlier role as TV's Batman.
The jokes on Family Guy deviate from random ridicule to Affectionate Parody, and most of them are pretty good mixtures of both. One of the most affectionate of them, however, would have to be "My Drunken Irish Dad" (as opposed to "The Freakin' FCC" (viewer discretion advised), which is essentially a giant Take That! to, well, the Federal Communications Commission). Except that it turns out the FCC actually liked it.
However, the affection by the third one has... waned. It's not so much that they grew to hate Star Wars as they began to grow frustrated with the format of forced storyline retread with jokes they had set up.
The Freakazoid!! segment "Toby Danger" parodied Jonny Quest TOS. They even went so far as to get Don Messick (Benton Quest) and Granville Van Dusen (Race Bannon) to do the voices of their parody characters.
Futurama is overall an affectionate parody of science fiction, and pop culture in general.
They assembled the entire (and then-living) cast of Star Trek: The Original Series for an episode, and spent 23 minutes lovingly mocking the show. Most of Futurama's writers are huge Star Trek fans, though series creator Matt Groening insists he's never seen an episode.
Except for James Doohan, who was replaced with Welshy. Briefly.
The character of Zapp Brannigan is an Affectionate Parody of Captain Kirk from Star Trek: The Original Series series. In a DVD commentary, producer David X. Cohen said his instructions to the writers when they sketched dialogue for Brannigan was, "Imagine if William Shatner actually captained the Starship Enterprise."
"Saturday Morning Fun Pit": Scooby Doo, Strawberry Shortcake and G.I. Joe (latter being censored by Nixon)
"Reincarnation": 20's-30's cartoons, 80's-90's 8-bit games and Americanized anime.
The Grim Adventures of Billy & Mandy is fond of this trope. They parody all the time and end up not making it look worse. A particularly affectionate one was "Hokey Monsters", a Pokémon parody, where they make it a card game and bring them to life. They pick at a few aspects of it but in the end it said Pokémon was still awesome. They've done many many others like Mary Poppins and Fantasia's "Night on Bald Mountain" segment.
Kim Possible seems to have been designed from the outset to ask the question "What if Buffy the Vampire Slayer was James Bond", leading to a "affectionate parody of spy movie conventions and superheroes" as part of its central concept.
Kim Possible did an affectionate parody of the 1960s Batman franchise with The Fearless Ferret, whose actor, Timothy North (voiced by Adam West), ended up being a space-case who thought the TV show was real. They also used the episode to poke fun at the upside-down kiss from Spider-Man.
The episode contained another level of affectionate parody, since it featured Ron as the young successor to a costumed legacy, with the original hero giving him constant advice and reprimands via radio. Ron's voice actor, Will Friedle, also voiced Terry McGinnis on Batman Beyond.
Nor was this Adam West's first go-round with such things, as on Batman: The Animated Series, he voiced the actor who played The Grey Ghost, a somewhat campy and clichéd costumed vigilante hero. Other appearances of the character implied that The Grey Ghost may have shared some of West's Large Ham tendencies.
Metalocalypse, the parody of death metal whose soundtrack album made those in the same genre it parodies stop and take notes. It helps that the creator is a huge fan of the music, even including other parodies of the genre in his previous show, Home Movies.
The Powerpuff Girls episode "I See a Funny Cartoon in Your Future" spoofs Rocky and Bullwinkle and includes not only a caricature of Jay Ward at the end but has June Foray (Rocky, Natasha) as the voice of the ep's villain.
Also of note is their episode parodying The Beatles, which was full of jokes and references that made it clear that they were very familiar with the band.
"Night of the Fright Hound" is a parody of Terminator, as well as the mech from Aliens
"Escape from Mystery Manor" is a parody of the Saw films.
The Simpsons episode "Homer's Barbershop Quartet" is an Affectionate Parody of the career of The Beatles in the form of Homer's 1980s barbershop quartet, the B'Sharps, that takes the world by storm in a similar fashion to the way the Beatles did. The career of the B'Sharps mirrors that of the Beatles in almost every way, including similar controversies, the complete hysteria surrounding them and band meltdowns. The producers even persuaded George Harrison to play along, giving him the perfect closing line; as he watches the B'Sharps imitate the famous last gig on the rooftop of Apple Corps that the Beatles played, he acerbically mutters, "It's Been Done," and drives off.
"Osama Bin Laden Has Farty Pants" is a paean to a classic Wartime Cartoon, especially Bugs Bunny's.
In the "Coon and Friends" trilogy, this is done twice between Cartman and Cthulhu: one, a tribute to My Neighbor Totoro, and the other is a nod to the Chuck Jones cartoon "Feed the Kitty". The original "Coon" episode also parodies The Dark Knight in the beginning.
A meta-example: the 20+ minute animation "Trey Gets Stoned" is one of both the show itself (seriously, the animation is indistinguishable) and Trey Parker and Matt Stone. Not surprising, since it was made by several fans.
Star vs. the Forces of Evil is an affectionate parody of the Magical Girl genre. Star Butterfly is a princess from another dimension, and has a magical wand that looks like a mashup of several wands other magicalgirls use. However whenever she casts a spell it usually has disastrous results, but she also fights monsters with her bare fists.