Shout-outs and references from the games in the Dragon Quest series.

Main Series

Dragon Quest

Pazuzu◊ is a reference to the Winged Monkeys from The Wonderful Wizard of Oz, who also served a sinister, evil sorcerer.

In the Soo village (NES version) you will meet Ed the talking horse. Additionally, a villager at night will mention that "his horse is a horse, of course of course".
At the Promitory of Olivia (NES version), you will hear the sad tale of Olivia and her lover Errol (now known as Eric). Bonus points that it is a seafaring tale.
The Gaia's Navel dungeon features a creepy hallway with talking heads in the walls telling the hero to, "go back," as he passes each one. This sequence happened in Labyrinth.
The green crab enemy is called a Crabber Dabber Doo.

In Chapter 3, Torneko can recruit a pair of mercenaries named Laurel and Hardie.
The kingdom of Gardenburgh was renamed Femiscyra in the retranslation and is a secluded island kingdom populated almost entirely by female warriors.
In the DS and Mobile remakes, the imposter "princess" is named Anya, after the "imposter" princess of the 1997 film Anastasia, which is kind of odd, given that the film was based on the events of the imposter named "Anna Anderson", whose DNA testing revealed that she was not the actual Russian grand-duchess Anastasia Nicholaevna Romanov.

King Albert and his chancellor Jeeves — aka Jeeves and Wooster.
Grandmaster Nimzo is named after Aron Nimzowitsch, a Latvian-born Danish unofficial grandmaster of chess. All of Nimzo's minions are named after chess pieces.
In one plot event, many citizens of Gotha are passed out on the floor. One of them, a nun, says the following in her sleep:
Zzz...
Sisterzzz are doing it for...
Zzz...
The Mysterious Dr Agon has many of Ned Flanders' verbal tics.
In the PS2 version, the names you could pick for the saber cat include Lynx, Peach, and Zorro.
One plot-based item is dubbed the 'Circle of Life'. When the psychic in Fortuna mentions it, she calls it "that toe-tapping number, the Cir-cle of Li-i-ife", despite it being a ring — not a song.
Later on, when the player actually collects the ring, the standard Get Item message box is altered slightly — instead, it says "It's the Circle of Life", a line direct from the song.
The ghostly Count Uptaten seems to enjoy imitating Count von Count. Of course, with a name like Count Up-To-Ten, it's probably expected.
Count Uptaten: Easy as vun, ha ha ha, twooo, ha ha ha, zree!
At the beginning of the game, Pankraz will suggest naming the main character Madason. If you actually choose that as your name, he will instead suggest Er dri ck.
King Korol. Say it out loud.
The Zenithians speak with Ye Olde Butcherede Englishe, just like the NPC's in the first game.

Dragon Quest Heroes: Rocket Slime contains shout-outs to other Square Enix-published series, such as a Platypunk ally named Ducktor Cid (a reference to the recurring character name in Final Fantasy) and the hero goes up against a tank with a treant-like appearance called Chrono Twigger (an obvious reference to Chrono Trigger), whose in-game logo even resembles the Chrono Trigger logo. These two are notable because the series referenced were formerly Square series, whereas Dragon Quest was an Enix series.
Dragon Quest Monsters has a breed of Slime called a Slimeborg. ^note Cyber Slime in modern localizations Resistance is futile.