Cassandra Nova Xavier is what the Shi'ar call "Mummudrai", the spirit that is the equal and opposite of a person. However, due to the amazing genetic potential of Professor Charles Xavier, his Mummudrai was able to create a physical form, effectively a twin.
While gestating in her mother, Sharon Xavier's, womb, Cassandra was recognized by Charles as an evil presence, and he pre-emptively tried to kill her, with his nascent psychic abilities. Cassandra was barely able to defend herself and the shock of the roiling battle caused her miscarriage. Though the doctors pronounced her stillborn, Cassandra in fact survived and spent the next decades as a growing mass of cells in a sewer wall, building a new body for herself and planning her revenge on her brother.
When she emerged, Cassandra located a secret "wild" Master Mold in the South American jungles that was able to adapt existing technology into a wide variety of lethal Sentinel forms. She convinced a cousin of Bolivar Trask to accompany her to the Master Mold, where his voice activated the control protocols. After killing Trask by merging herself into his body, she dispatched giant Sentinels to Genosha, resulting in the genocidal massacre of over sixteen million mutants, including Magneto. Her Wild Sentinels also attacked the X-Wing, downing it with Cyclops, Wolverine and their passenger Ugly John aboard. The X-Men subdued Nova, but lost Ugly John. Wolverine severed Cassandra's vocal cords and she was brought to the Institute, where she began to exert telekinetic and telepathic control over the X-Men, making her way to Cerebra by phasing in an effort to destroy all mutants. Then Emma Frost snapped her neck, stunning Cassandra, who was finally put down by six gunshots from Charles.
What no one realized at the time was that just before the shots, Cassandra switched her mind into Charles's body and vice versa. Using Charles's form, Cassandra "outed" him and the X-Men to the world, then left Earth with Lilandra for a "vacation." While in the Shi'ar Empire, Cassandra used her powers to take control of the Imperial Fleet and began to destroy the Empire. Lilandra made for Earth, but Cassandra destroyed the ship, and upon arrival back at the Institute took down the Superguardians as well. By this point, Cassandra (in Charles's body) had constructed a psychic monster around herself, seemingly made up of the flailing body parts of all the people she had absorbed or controlled.
After beating off all comers, Cassandra again came to Cerebra. She tried to use Cerebra to access the minds of all Earth's mutants, but Charles's mind was waiting for her (put there by Jean Grey) and he forced her out of his body. Formless and with no life support, Cassandra flailed about until Emma came in with Cassandra's body, which the entity entered, only to be trapped inside, as her real body was dead, and this body was the Imperial Superguardian shapeshifter Stuff. Her mind has been blanked and she is being re-educated by mental simulcra of Professor X and Phoenix.
In the last act of desperation, Nova used her powers to plant a suggestion deep into Emma's mind. She played on her fears, doubts and guilt, to create a psychic delusion in which Emma believed that Nova had returned and recruited her into a new Hellfire Club, alongside with Sebastian Shaw and Negasonic Teenage Warhead. Emma then tortured the X-Men with illusions and incited Kitty Pryde to release Stuff from its lockbox. Freed, Nova sought a new host, she tried to possess Kitty's body, but didn't succeed, and apparently escaped. Sydren from the S.W.O.R.D. studied Emma's mind and didn't find any trace of Nova's mind.
Cassandra possesses telepathy comparable to Charles Xavier. After copying the DNA of Charles Xavier, the mummudrai Cassandra Nova accessed the full spectrum of latent mutant functions in his genome (this means she has the powers of Charles Xavier, the ones he could have had and the ones he might receive, as a result of latent mutation), granting itself vast psionic powers. These powers include: telepathy, telekinesis, and the ability to release an astral form, which she focuses both her telepathy and telekinesis. She has all the powers of the "average" mummudrai as well.
DNA Duplication: able to copy the DNA of sentient beings and use it to construct physical bodies for themselves. Also capable of accessing the full spectrum of latent mutant functions in ones genome.
DNA Manipulation: can manipulate the DNA of others, breaking it down at the molecular level.
Jumpstart: After analyzing the DNA of another superhuman mutant, Cassandra is able to selectively evolve their existing genetic traits as well as catalyze the untapped genetic potential of latent mutants. Once begun, the procedure is irreversible and can often result in unpredictable side effects.
Phasing: ability to pass through solid matter by passing her atoms through the spaces between the atoms of the object through which she is moving. In this way she and the object through which she is passing can temporarily merge without interacting, and each is unharmed when Cassandra has finished passing through the object. This process is called "phasing". When Cassandra is phasing she is intangible.
Metahuman Regeneration: She regenerates and heals hundreds of times faster than a normal human. Thanks to this superhumanly regenerative "healing factor," she has been able to completely recover from injuries which would prove fatal to most humans, even those with superhuman abilities. She can regenerate organs such as eyes or large portions of flesh, regenerate limbs, such as feet and arms, which have been completely severed.
Trask DNA: Using her powers, she was able to duplicate the Trask DNA, and therefore include herself in the Prime Command Protocols of the Sentinels, "Preserve Trask DNA".
Astral Form Projection: ability to release her astral form, which she uses to focus her telepathy and telekinesis.
Telepathy: can read minds and project her thoughts into other minds within a vast, potentially limitless radius.
Telepathic Cloak: Can mask her presence from being detected by others. Her abilities can at times go undetected or be counteracted by other more powerful telepaths depending on their level of skill in using their own psi abilities. She can extend these defenses to others around her as well.
Mind Control: ability to control the minds of others upon mere concentration.
Mind Possession: ability to possess the mind of another, and use that beings body as your own
Mind Alteration: ability to alter the minds of others by force of will.
Psionic Shield: ability to erect a psychic shield for protection of himself and of others minds
Telepathic Illusions: ability to create illusions to make herself seem to be invisible, look like someone else, or make others experience events that are not truly happening.
Mental Paralysis: ability to induce temporary mental or physical paralysis
Mental Amnesia: Can erase any awareness of particular memories or cause total amnesia.
Psionic Blasts: can project psionic force bolts which have no physical effects but which can affect a victim's mind so as to cause the victim pain or unconsciousness and turning someone brain-dead.
Astral Projection: can project her astral form from her body onto astral planes or the physical planes. In the physical plane she can only travel in astral form over short distances. In the astral plane, she can mentally create psionic objects and manipulate the aspects of her environment.
Mind Transferral: able to transfer both her mind and powers into other host bodies should her own physical body be somehow killed
Mental Detection: can sense the presence of another superhuman mutant within a small but as yet undefined radius of herself by perceiving the distinctive mental radiations emitted by such a being.
Telekinesis: possesses telekinetic abilities enabling her to levitate and manipulate living beings, inanimate objects, and to some extent energy psionically. She can levitate herself or other persons or project a telekinetic shield capable of withstanding missile blasts. By focusing her mental energy at a specific target, she can release devastating force blasts.
It was suggested that Nova used her vast psionic powers to awaken or even create Emma Frost's Secondary Mutation which granted her the ability to turn herself into "living diamond".
In order to disable Charles Xavier while being in his body, Cassandra Nova infected her own body (hosting Charles) by Motor Neuron disease, a rapid form of Alzheimer's disease and Creutzfeld-Jacob disease.