Norm was supposedly created by Dr. Heinz Doofenshmirtz after realizing that the only way to destroy his lifetime nemesis Perry the Platypus was to find the true enemy of the platypus: not any weapon or ray gun or duplicatable stunt seen on television, but man. Norm chased after Perry through Danville, trying to destroy him. During Phineas and Ferb's chariot race, Norm ran into the ox statue outside Paul Bunyan's Pancake Haus, dislodging the ox head and causing it to fall on him. Still wearing the ox head, Norm resumed his pursuit of Perry, and began chasing Phineas and Ferb's chariot after Phineas picked up Perry. Seeing Norm behind them, they think Norm is the Minotaur from Greek mythology.
Still chasing after the chariot, Norm enters the National History Museum, and towers over Candace. Believing him to be human, she yells at him, as Perry switches him off. Falling to the ground, Candacе believes she has turned him to stone. After everybody leaves, Doofenshmirtz returns to turn Norm on, but not before Perry puts a platypus hat over him. Doofenshmirtz was unable to remove the hat and Norm thinks that he is a platypus and therefore went chasing him. ("Greece Lightning").
Working with Agent P
"That's it? You just want to borrow Norm, my giant robot man? Fine, knock yourself out." — Dr. Doofenshmirtz[source]
Later, Perry the Platypus asks Doofenshmirtz to borrow Norm for a mission to destroy a CD containing footage of Perry's exploits. Perry takes Norm and rides in his head, stealing the CD from Candace Flynn's hand at the Flynn-Fletcher house. They run back to return the CD to the Agency HQ, but are pursued by Phineas, Ferb, and Candace. As they are running, Norm informs Perry he is running low on oil.
Stopping at an oil-depot, Norm is filled back up with oil, but because the three return to catch them; Agent P does not put the oil cap on. Running away causes Norm to leak profusely. Then, heading to a bridge, Norm is stuck in a predicament as he is hanging by his legs on the split bridge. Falling to the lake, Norm escapes it and becomes part of The Agency even though Monogram thought it was a little weird because he wasn't an animal. Monogram then states "We should fire him." Carl gets his clipboard and responds "I am already on it, Sir" ("Traffic Cam Caper").
After being fired from the Agency, Norm returns to the employ of Dr. Doofenshmirtz, and is soon helping the Doctor build an evil country to call his own, Doofania. He provides the obligatory "Whatcha doin'?" moment that Isabella normally says, comments on how Heinz is "a little old to be building a fort", drills to help Doof, and is present at the unveiling of the country itself. He also plays the instrumental accompaniment to the national anthem, Hail Doofania!, using his built-in record player. The country soon sinks to the bottom of the bay from Phineas and Ferb's Big idea for Isabella, and lacking anything better to do, he and Doofenshmirtz attempt and fail at playing a game of Hide-and-Seek. However, it is soon discovered that Norm doesn't understand hide-and-seek, trying to hide behind poles. After some explaining, he hides well behind boxes, though when Doofenshmirtz says "I wonder where Norm is?" he responds "I'm right here, sir!" ("Hail Doofania!").
Cooking For L.O.V.E.M.U.F.F.I.N.
Norm: Well next time you can do all the cooking, and I'll stand around coming up with evil plans that ultimately fail!
Awkward silence while they stare at Norm.
Dr. Doofenshmirtz: Wow. Cuttin' deep, man.
Some time later, Norm helps Doofenshmirtz cook for his press meeting with the evil group League Of Villainous Evildoers Maniacally United For Frightening Investment's in Naughtiness (L.O.V.E.M.U.F.F.I.N.). Norm seems to have developed an attitude, being defiant towards the Doctor and pointing out his flaws ("Nerdy Dancin'").
Taking Over for Doofenshmirtz
When Dr. Doof was on jury duty, Norm was placed in charge of DEI, and caught Perry with a muffin. He then revealed that instead of making an inator, he would use himself to destroy the Tri-State Area. Perry used the nanobots invented by Phineas and Ferb to create counter weapons to those Norm was using, and ultimately used them to make a giant acorn for the squirrel that Norm has to use being powered properly turning his power off, and leaving Norm to fall to his defeat. It is still unknown if Norm seemingly "self destructed" or hit the ground faster than expected after his defeat as we only see the squirrel powering Norm after he falls ("Norm Unleashed"). However in Where's Perry?, he is seen intact so either he was not destroyed or he was rebuilt by Doofenshmirtz.
Hyper transportation mode (aka, rocket skates)
Basic sound system (internally-stored record player and speakers)
Extends his arms and legs
Can transform into a pickup truck (shape-shifting)
Initially, Norm could only speak in stereotypical "American Dream Husband" phrases, though he could also say "The enemy of the platypus is man" and state that he needs to be charged or filled with gas. As time has passed, Norm's artificial intelligence has grown, and he is now able to react to conversations on a more human-like level, albeit by still using stereotypical phrases. Norm is still unable to realistically imitate human behavior. Recently, he does not seem to like Doofenshmirtz as much, pointing out that his schemes always fail, but helps Doofenshmirtz with his scheme anyway. ("Nerdy Dancin'") Norm wants Doofenshmirtz to make him a girlfriend/wife out of blue raspberry Popsicle sticks. ("Undercover Carl") Norm looks up to Doofenshmirtz as a father. ("A Real Boy")
Norm is still kept by Heinz Doofenshmirtz in his apartment even though he failed his mission. This may either be because Doofenshmirtz does like Norm or he enslaves him into servitude. This could also be Norm refusing to leave due to him viewing Doof as a father.
In Hail Doofania!, Norm's mouth stays frozen, and whenever he talks, a light would flash in his mouth, causing his "teeth" to flash from white to neon green and back again. Oddly, in Traffic Cam Caper, he is able to change facial expression (i.e. at the very end, his mouth forms a straight line after he says "I'm Norm".)
When Doofania was sank, Norm falls in the water, yet he can still talk, even though he is a robot, though this may be because he runs on squirrel power ("Hail Doofania!").
He wants to be a real boy, and also wants Heinz Doofenshmirtz be his father ("A Real Boy").
In the beginning, when he talked, his mouth flashed green, but now it flashes white when he talks.
It has been revealed that Norm has a self-destruct button, but Doofenshmirtz never told him where it is, so Norm wouldn't pick at it ("Ferb Latin").
He has been very rude to Doofenshmirtz before. In "Hail Doofania!" Norm says that Doofenshmirtz is "a little old to be building a fort." He often points out all of Doofenshmirtz's flaws (Nerdy Dancing), insults Doof in front of his fellow evil-doers and when Doof tells Norm that he is terrible at cooking Norm retorts "Next time you can do all the cooking while I will stand around making evil schemes that always ultimately fail!"
Norm seems to really like celebrating New Years as he keeps celebrating the event even if it's still not midnight yet ("Happy New Year!")
Norm keeps a set of heads in a cupboard that are used for different personalities, (happy, sad etc) but all of them are smiling ("A Real Boy").
Get Smart (TV series) - Evil organization, KAOS, invents a robot, Hymie, that they plan will be able to kill Maxwell Smart, but fails, like Norm does to Perry. Later in the series, Hymie is taken and used by the good organization, CONTROL, to be used as Max's partner, like how Perry uses Norm.
Moviefone - His voice and diction is like the one used for "Moviefone," a phone service to get film info before the Internet became available.
Transformers - In Undercover Carl, Norm turns into a pickup truck. It is an allusion to the Transformers franchise in which robots transform into various vehicles.
The World of Norm - The book, "The World of Norm," is dedicated to Norm, the oversized robot.