Basic Trope: For some reason shapeshifting affects the way the shapeshifter thinks and behaves.
Straight: Bob and Alice have their minds exchanged by a Mad Scientist. Despite some initial confusion and discomfort, they rapidly adjust to their new bodies. After a month or two, even though they remember their old lives, you would not be able to tell from their mannerisms or emotional reactions that they'd ever been the opposite gender.
Exaggerated: Bob has the ability to turn into a wolf, gaining the instincts of that form. After a week in that form, he forgets he was ever human.
A character's sexual orientation changes after a gender bender, but not their behavior or personality.
A human that is turned into a wolf develops a craving for raw meat, but nothing else.
The new body's hormones and outside social pressure to conform to the new shape's role combine to affect the shifter's attitudes.
The magic in a Baleful Polymorph curse slowly erodes the victim's memories and personality to make it ever harder for them to seek out or accept a cure.
Bob's personality is like the Animal Stereotype of a wolf, so a certain magic spell turns him into a wolf.
Bob has been acting more and more like a normal dog since he shifted into that form—but it's actually an put-on so that the villain will feel free to speak in front of him and spill his plans.
When Alice is turned into a cat, she doesn't gain the instincts of a cat i.e. she lacks the grace to always land on her feet.
Once the villain has been sent to jail, Bob is told that he can turn back now, but he refuses, because being a dog is more comfortable for him now.
After spending sufficient time as a cat, Alice picks it up.
Macho action hero Bob is turned into a woman. He immediately begins acting out the most demeaning feminine stereotypes and insists that his name is now Missy. Several other characters point out that the Applied Phlebotinum involved doesn't affect the victim's personality...Missy doesn't believe them.
"My new lady parts compel me to enjoy shopping for frilly lingerie!"
Alice dyes her hair to a shade similar to Bob's, and immediately immediately begins acting out the most demeaning masculine stereotypes and calls herself Adam.
Zig Zagged: Bob has been acting more and more like a normal dog since he shifted into that shape, but it was an act to throw the villain off guard, but Bob doesn't change back once the villain is captured, but he retains mostly human mannerisms, but then he becomes leader of a pack of feral dogs and renounces his humanity, but....
Averted: The rules of magic in this universe state that the body, mind and soul of a person are separate targets for transformation spells. Any behavioral changes in a physically transformed person are purely down to actual experiences in the new body.
Enforced: The writer wants shapeshifting to be a rare occurrence in her story's universe, so makes sure it has this downside.
Lampshaded: "Don't be silly! Turning into a dog doesn't affec—Squirrel!"
Invoked: Helga the Hot includes a personality-eroding effect in her Baleful Polymorph spells to really screw her victims over.
Exploited: Knowing that this effect exists, Charlie secretly inflicts a Gender Bender on Bob and the other boys in his class, in hope of having a better chance of getting dates.
Defied: "This amulet I wear prevents me from losing my true self, no matter my current form."
Discussed: "Bob's been acting kind of...funny ever since he turned into a dog, don't you think?""
Conversed: "Given that Fanfic Writer X always has her Gender Bender victims totally embrace their femininity by the end of the story, regardless of their original personalities, I'm going to presume Author Appeal."
Deconstructed: So many people are scared of the change affecting their mind that the only people who use the device are people that want this sort of thing; otherkin for instance.
Played For Laughs: Bob retains personality traits of shapes he's shifted into for a few minutes after returning to human, but it's just a set-up for episode-ending jokes.
Played For Drama: Bob's tendency to become more deeply immersed in the personality of his alternate forms is a serious problem, and suspense is built in long story-lines as to whether or not he'll be able to change back in time.