The four Pevensie children are the main characters in The Lion, The Witch and the Wardrobe, the first-published book of The Chronicles of Narnia. At the end of that book they are crowned Kings and Queens of Narnia.
Peter is the eldest of the four Pevensie children. He is depicted as a natural leader, though somewhat headstrong. He sides with Aslan throughout the first book and, upon their victory over the White Witch, is crowned High King Peter the Magnificent. He appears in major roles in The Lion, the Witch, and the Wardrobe and Prince Caspian, and in minor roles in The Horse and His Boy and The Last Battle.
Peter is depicted in badfic as a reckless leader with no consideration for others. He is often slashed with his brother Edmund (see incest) or with Caspian X. In the former he is usually the dominant partner, in the latter he is more usually the submissive, although this largely depends on the badficcer's depiction of Caspian. He is often made out to be ruled by passion and to not have an actual functioning brain outside of the rather rudimentary one in his trousers.
Susan is the second-oldest of the four children. She first appears in The Lion, The Witch and the Wardrobe, and has major roles in that book and in Prince Caspian, as well as a minor role in The Horse and His Boy. She was crowned Queen Susan the Gentle, and famed for her skill as an archer. She was also the possessor of a magical horn (given to her by Father Christmas) which, when blown, would summon help.
She lost faith in Narnia by the end of the series, as revealed in The Last Battle, although she was not dead yet and as Aslan has stated that a queen of Narnia will always be a queen, it's likely she'll regain in her faith in Narnia. In the Movies she is played by Anna Popplewell.
In badfic, Susan is often paired with Caspian X or with her sister, Lucy Pevensie. She is also frequently made out to be the intolerant bitch of the family upon discovering incest between her brothers or a relationship between either (or both) brothers and Caspian X. This is an interesting take on the Designated Misogynistic Bastard, but still a charge. Love triangles or even squares between these four are common.
Conversely, she is also often entirely approving and encouraging of three-in-a-bed romps between her brothers and Caspian. A complex character in canon, in badfic, Susan is positively schizophrenic.
Edmund is the third-oldest child of the Pevensie family. He is first introduced in the book The Lion, The Witch, and the Wardrobe.
Edmund has a reputation as the thinker of the group. While he initially supports the White Witch, he rejoins his brother and sisters to help defeat her by the end of the book, and is crowned King Edmund the Just.
He also appears in major roles in the books Prince Caspian and The Voyage of the Dawn Treader, and in minor appearances in The Horse and His Boy and The Last Battle.
In the Movies, Edmund has so far been played by Skandar Keynes. He has a huge following of fangirls, who tend to call him Skandalous.
There appears to be very little objection to incest or slash in the Narnia fanbase, and Edmund is most frequently paired either with his brother Peter Pevensie or with Caspian X. Real Person fic featuring these three young male actors is also rife. A fanon convention appears to be that Edmund was openly homosexual during the Golden Age of Narnia. In bad slash, Edmund is often extremely sexually precocious, and the more submissive member of a pairing.
In Sue stories, he is normally a bad tempered person who falls for the Sue immediately but doesn't show it.
Lucy is the youngest of the four Pevensie children. She initially discovers the way into Narnia via the wardrobe, and throughout the books she appears in she has the most faith in Narnia and in Aslan. She first appears in The Lion, the Witch and the Wardrobe, and has a major role in that book and in Prince Caspian and The Voyage of the Dawn Treader, and a minor role in The Horse and His Boy and The Last Battle. She was crowned Queen Lucy the Valiant.
In the Movies, she is played by Georgie Henley.
Lucy is usually Too Dumb To Live in badfic, mainly in the name of displaying either how naive and sweet she is, or how heroic she is. On the rare occasions she is put into a romantic pairing, it is often incestuous slash with her sister Susan, or het fic, paired with Mr. Tumnus, the faun who is the first Narnian she meets. This latter is usually introduced by an author who has had too much sugar as 'like, totally crack!fic'.