Wizards are species of magic-wielding characters who appear in the Shrek franchise. While they've shown to be common in the first film, their appearances became far less frequent (completely absent) in future installments.
Merlin is the only wizard to have appeared in the sequels.
The main antagonist in these games is a version of Merlin, who's an evil wizard. In the X-Box version, he kidnaps Fiona for no reason; in the GameCube port, he kidnaps Fiona because the Wicked Ice Queen stole his crystal ball and trapped him.
Another version of Merlin, notably more heroic, appears in this film. He gives shelter to Shrek, Donkey, Puss and Artie when they get stranded. During their stay, he performs a magic trick on a fireplace to delve into their minds. Later on he helps the four get back to Far Far Away, using his teleportation spell. Unfortunately because of Merlin's old age, his magic does contain side effects, notably switching the souls of Puss and Donkey. At the end of the film, he tries to reverse the spell, only to accidentally swap their tails in exchange for their souls.
Wizards are stereo-typically old, bearded, wear long robes embroidered with stars, and have tall, pointy hats.