In this series, a few vampires have "special abilities" or powers. It can be a useless power like compassion (Ma-Ti) or an interesting power like the ability to destroy all human senses (sight, taste, smell, touch, hearing, etc) like Alec. Few of these work on Bella because she is SPESHUL; Jasper, Alice, and Marcus are effective against her, but apparently no one else was.
According to Edward's (?) theory, salient personality traits one had as a human are augmented when one is vamped, turning these traits into powers. For example, Jasper might have been very empathetic and persuasive as a human, so as a vampire, he can sense feelings and alter them. Edward may have been very perceptive, so as a vampire he can read minds. Alice might have been schizophrenic as a human, which explains....actually not a whole heck of a lot. And of course, since Bella was clumsy, her transformation made her super-graceful, even for a vampire. This theory is of course flawed in its suggestion that any of the Cullens have ever had salient personality traits.
Aro: Aro has the ability to know every thought you have had in your life by touching your hand. There are ways to portray this without making him look like a child molester, but the movie conveniently avoids them all.
Marcus: Senses (giggle) relationships. May or may not involve a day-job as a celebrity gossip columnist.
Alec: Can destroy any human sense, rendering his victims blind, deaf, and numb. (Presumably as a human he was very, very boring.)
Jane: Can cause pain just by looking at you. Has potential, but would be much cooler if not for the fact that a sad-looking puppy can do the same. Also, Edward did not scream when being tortured by Jane, so her power is inferior to the Cruciatus Curse. It was theorized that it worked by targeting the pain receptors in the brain, but this was Jossed by the fact that Bella's telepathic shield blocks it.
Chelsea: Can see relationships and influence them. (This makes her twice as useful as Marcus, so heaven only knows why he's still around. Chelsea may have been a psychiatrist or internet dating site in her pre-Meyerpire life, though some theorize that she simply played MASH far too often.) Even though she's twice as useful as Marcus, we can't have female empowerment, now can we?
Renata: Makes you disoriented so that people avoid you. (Presumably she was hide-and-seek champion as a child.)
Stalker Tracker (There is no logical explanation for this one. Just back away slowly.)
Heidi: Attracts people by making them see her as exactly what they desire. (Appears to be exactly like the auto-beautification every vampire undergoes, but specialer...somehow.)
Didyme: Creates aura of happiness. (No comment...) Was probably a pizza in past life.
The Olympic Coven: Cullens Edit
Carlisle: Is compassionate. Yes, really.
Edward: Basic mind-reader, nothing original here. Is also super quick for some reason, even though all Meyerpires are fast.
Jasper: Can control people's mood. Kinda like drugs. The side effect of this power is that using it makes him extremely constipated.
Alice: Can see into the future...sometimes...when it's convenient...and no werewolves are involved...and the phase of the moon is right...assuming no random factors are introduced. Basically useless, except when it's not.
Bella: Immunity to mental powers, where "mental" means "chosen according to some criteria I pulled out of my butt, which may or may not haveanything to do with anything." As a Meyerpire (yes, the previous was her super speshul power from when she was still a human.. I'm serious..), she can create a mental shield around people, breaking the powers of most notably Jane, and (after stupidly quick mastery of her powers, 'cause she's speshul like that) later she can shield almost her entire 'faction' of sorts in the movie.
Renesmee: Can show her thoughts or memories to anyone, regardless of their defenses, but only by touching them. Yeah, real useful. But maybe it's actually mind control, as everyone who is touched by her seems to gain a creepy amount of devotion to her (a la Damien).
Esme: Can love passionately...Again, really? At least Carlisle can use his "power" to resist human blood.
Emmett: Strength. (You know, like every other vampire, but again...specialer.)
Tenacity. Beauty and the ability to be the biggest bitch.
The Irish Coven: Edit
Siobhan: May or may not have the ability to make things to turn out her way by willing it so.
Maggie: Can tell if a person is lying. Been there, done that, move along. It is unknown if Maggie is also able to gauge whether or not a person is sitting down.
The Egyptian Coven: Edit
Benjamin: Can manipulate the elements of earth, air, fire, and water. (This doesn't rip off "House of Night" or "Vampire Academy" at all! *sarcasm hand raised*) It is currently unknown whether or not he is also able to manipulate the elements of style or heart. Aang could also kick his ass.
The Denali Coven: Edit
Eleazar: Can pick out the people who will have powers when they are turned into vampires.
Kate: Is electrically charged, so that anyone who touches her (vampires included) collapses. She could probably also be used to charge flashlights, but as of Breaking Dawn this has not been tried. Probably not however, since her power is useless against Bella, which makes her less powerful than the Energizer Bunny.
The Amazon Coven: Edit
Zafrina: Can create mental illusions in the minds of others, just like LSD.
The European Nomads: Edit
Alistair: Another tracker. Yawn.
Charles: Maggie all over again.
The American NomadsEdit
James: Yet another tracker. (Only he uses his nose or something.)
Victoria: Has a sense for the safest place to hide. And yet she still gets killed.