Apparently, Twilight Sparkle from My Little Pony: Friendship Is Magic and Pretty Pretty Pegasus fanatic Raven are both voiced by Tara Strong. In addition to that, "Books" has Raven expounding the virtues of books to the team, much like Twilight Sparkle at one point or another.
The circus flashback itself is a reference to Robin's backstory. This is in line with a previous reference to the circus in the original Teen Titans series when Raven entered Robin's mind. It should be noted that the episode baits viewers who know this into predicting that Robin stopped relaxing after his parents were killed just like in the comics, only to reveal that it's because the animals kept stealing his stuff.
One of Cyborg's bodies is shaped like one of the Voltron lions in leg mode. Another one is DCAU's Brainiac ("too brainy").
When Beast Boy uses a vacuum to suck up Cyborg's soul, the music resembles the Ghostbusters theme.
Starfire's dress-making skills and the end result is a lot like what the character Giselle does for a hobby in Enchanted.
When the suits start attacking, Robin's and Raven's suits slack off and dance to the "Yeah! Woo!" loop.
At the start of "Ghost Boy", Beast Boy pops out of Robin's closet as a Velociraptor using the Jurassic Park T. Rex's roar.
"La Larva de Amor" has several during the milk mustache contest, such as Robin becoming Mario, Raven becoming Gandalf and Beast Boy becoming Chewbacca, complete with Bowcaster. Also, Cyborg resembles B.A. Baracus.
Of the many references to other DC characters in the series, perhaps the most potentially impactful on the story was Beast Boy finding a Green Lantern ring in the couch at the start of "La Larva de Amor". Of course, as he was looking for something else, he tossed it aside.
Apparently, the skeleton reaching for water under Starfire's bed was Deadman (Boston Brand).
He later talks about Webster and The Pointer Sisters.
He mentions that the actor who played Webster "was like 40 in real life". Cyborg may have confused him with Gary Coleman, who starred in Diff'rent Strokes.
When Cyborg is hooked up to the Titans Tower mainframe, he loses his humanity and starts acting more like HAL 9000. He even starts speaking in a Creepy Monotone, only shows his cybernetic eye, and utters the famous line "I'm sorry, but I cannot do that".
He also starts filling the Tower with a green gas that looks like the neurotoxin from Portal.
A reference to The Brave Little Toaster is made in the end, where Robin's Lampy, Starfire's Toaster, and Raven's Kirby. No wonder that scene was so disturbing.
When attempting to communicate to Cyborg via pictures, Raven draws Darth Vader's helmet to represent "force". For clarification, the message, in this particular case, is that Cyborg always force her to have a good time.
One of the ponies Raven plays with has a blue mane and pink fur, like Firefly from generation 1 of My Little Pony. Firefly happens to be the favorite pony of Lauren Faust, who created Friendship is Magic, where Raven's voice actress, Tara Strong, plays the lead pony.
Said giant foods intro is a clear shout out to Pacific Rim.
The display on Cyborg's monitor in "Matched" is in the same style as the stage select in Mega Man 2, and just as he activates the machine, there's a pixel version of the heart shot from The Powerpuff Girls.
Robin's flashback in "Baby Hands" has all the Titans in their original outfits.
In "Caramel Apples", there are quite a few:
Robin's inspirational speech to Cyborg and Beast Boy when they're trapped in Hell is rounded off by saying, "...and most important, HEART!" It serves as an Actor Allusion for Scott Menville, his voice actor.
Control Freak being a male fan of Pretty Pretty Pegasus is a Shout-Out to Bronies.
A little later, Starfire hits him with a Shoryuken.
When the Titans are transported to the Pretty Pretty Pegasus show, Raven's face resembles the "Awesome Smiley"◊ as she floats off screen.
The first few notes that play before the Pegasi start the "Friendship Song" resemble the main theme of Tiny Toon Adventures. Also, when she's about to sing, Sparkle Face's eyes begin to cross extremely similarly to Pinkie Pie when she did it in the My Little Pony: Friendship Is Magic episode "Party of One".
In "Salty Codgers", the gravestones during Death's Musical number include Boston Brand, Jason Todd, Martha & Thomas Wayne, and Zod.
In "Beast Man", you can see Dr. Manhattan on the magazine Raven reads to infuriate "The Man".
In "Thanksgiving", the Imagine Spot used to illustrate Beast Boy's explanation on why there are more rats resembles a scene from the 1954 Disney cartoon Pigs Is Pigs, replacing the Explosive Breeder Irish jigging guinea pigs with the rats.
In "Boys vs. Girls", Beast Boy briefly morphs into the mutant motorcycle rider on the cover of The Ramones' final live album We're Outta Here!
Raven is a ghost in the Pac-Man parody Circle Guy.
Cyborg ends up in the Spy Hunter parody Pie Hunter.
Robin parodies Super Mario Bros., even injuring his head by repeatedly bashing on blocks for cash and pointing out how gross the sewage pipes are.
When fighting Cinderblock on a motorcycle, Robin bounces the end of his staff off the ground like the biker gang members in AKIRA do with lead pipes.
"And The Award For Sound Design Goes To Rob":
The box that the Whisperer uses to remove all sound from the world looks a lot like the box from the Hush episode of Buffy the Vampire Slayer.
When the Titans create their own sounds to replace the missing ones, Starfire makes Silkie go "Hey, hey, hey!" like Fat Albert.
On "Leg Day", each Teen Titan (sans Beast Boy) has at least one transformation sequence taken out directly from Sailor Moon. Cyborg has Moon Prism Power, Starfire has Jupiter Power and Venus Power, and Robin has Moon Crystal Power, Moon Cosmic Power and Mercury Power.
In "Two Parter: Part One", one of the items in display at the Hall of Justice is an orange oven mitt. Possibly a reference to The Flaming C?
Two Parter: Part Two has Cyborg saving the Justice League by using time travel via making Apokolips rotate in the opposite direction, much like how Superman did the same thing on Earth in Superman: The Movie. They even mention that Superman did it.
Among numerous other shout-outs to other slapstick cartoons such as Looney Tunes, during the events of "Squash and Stretch" Cyborg turns on the TV, which shows green and purple Gumball and Darwinlookalikes engaging in Wile E. Coyote vs. Road Runner antics on the screen. Cartoon Network had a promotion where kids could record themselves and possibly end on TV. One girl sent a video that actually pointed this out, making for a rare meta-lampshading.
The episode "Beast Boy's St. Patrick's Day Luck And It's Bad" has a Dragon Ball-esque leprechaun fight.
Each of the five "Island Adventure" episodes spoofs a different "stuck on a Deserted Island" show or movie:
"Coconut Cream Pie" has the Titans turn into characters from Gilligan's Island. Beast Boy being Gilligan, Robin and Cyborg being the Professor and Skipper, and Raven and Starfire being Mary-Ann and Ginger.
"Pure Protein" spoofs Survivor, with Robin forcing the others to do challenges. When they won't play along, he calls an Expy of the Predator to hunt them down.
"Open Door Policy" references Jurassic Park when the Titans discover dinosaurs in the island. The suggestion of building a theme park is brought up, but rejected because of the possibility of it going wrong. Also, Robin talks about Velociraptors being able to open doors.
"Crazy Desire Island" is a parody of Fantasy Island, with Robin as Mr. Roarke.
"The Titans Show" spoofs The Truman Show, revealing that the island was a fake set build by Control Freak and that the Titans were being secretly filmed for his amusement and that of the show's other villains.
In one scene of "The Titans Show", the gang argues about what Beast Boy's ass-freckle looks like with Beast Boy saying it looks like Mickey Mouse while Robin says it's obviously "two bears high-fiving".
The whole plot of "Booty Scooty" is a reference to The Goonies, and the opening of the titular dance song is awfully similar to "Turn Down For What" by DJ Snake