Professor X

Charles Francis Xavier is a psychic mutant that goes by the codename Professor X.

Powers
Professor X is an Omega Level telepath and possesses vast psionic powers:

Telepathy: Professor X is able to read mind and project his own thoughts into the minds of others within a 250 mile radius while on Earth. With extreme effort he can greatly extend that radius. When synched with Cerebro or Cerebra, he can connect to every mind on a planet. After he was thrown into the M'Kraan Crystal, it not only restored his mutation, but made his telepathy more powerful than it has been previously, thereby making him the world's most powerful telepath once again. Professor X formerly also possessed low-level telekinetic abilities, though these seem to no longer exist. They seem to be part of his genes however, as Cassandra Nova has telekinetic abilities and is basically a clone of Xavier.
 * Telepathic Illusion: the ability to create realistic telepathic illusions and cause people to experience events which are not actually occurring.
 * Telepathic Cloak: he can mask his presence from being detected by others. His abilities cat at times go undetected or be counteracted by other more powerful telepaths depending on their level of skill in using their own psi abilities. He can extend these defenses to other around him as well.
 * Psi Link: the ability to develop a mental link with any person which remains as a connection to that individual.
 * Telepathic Camouflage: the ability to mask himself, and other peoples' presence from those around him. He can telepathically disguise himself, making his appearance to those around him quite different (changing the appearance of clothing, as well as more involved disguising).
 * Mind Blast: the ability to place large amounts of information in another's mind, causing pain.
 * Mind Control: the ability to control the minds of others upon mere concentration. This power can allow him to completely shut down several people's minds, making it appear as if time has stopped.
 * Mind Possession: the ability to possess the mind of another, and use that being's body as his own.
 * Mind Alteration: the ability to alter the mind of others by force of will.
 * Mental Amnesia: the ability to cause loss of particular memories and amnesia in another person or even in a group of people.
 * Psionic Shield: the ability to erect a psychic shield for protection of himself and of other minds.
 * Psionic Blasts: he 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 can even kill an adversary.
 * Astral Projection: the ability to Astral Travel and communicate with others astrally through his own will, or through contact with the thoughts and memories of others. In the astral realm, he can use his powers to create "ectoplasmic" objects. He cannot engage in long range astral projection on the earthly plane.
 * Mental Detection: he can sense the presence of another superhuman mutant within a small but as yet undefined radius of himself by perceiving the distinctive mental radiations emitted by such a being.
 * Mind Transferal: he is able to transfer both his mind and powers into other host bodies if his own physical body could be somehow killed.
 * Absorb Information: the ability to quickly process and store information, by mental transference.

Telekinesis: Professor X possessed telekinetic abilities enabling him to manipulate matter on a low level with the energy of his thoughts.

Weaknesses
Paraplegic (Formerly): Professor X has been normally unable to walk due to spinal damage, originally suffered while combating Lucifer.

Dark Side: Xavier was shown to have a dark side, a part of himself that he struggles to suppress. Perhaps the most notable appearance of this was the entity Onslaught, which was a physical manifestation of that dark side. Also, Onslaught was created in the most violent act Xavier claimed to have done: Erasing the mind of Magneto. Once the X-Men fought images of the original team, which had been created by what Xavier said was his "evil self ... who would use his powers for personal gain and conquest," which he said he was normally able to keep in check.

In other instances, Xavier was shown to be secretive and manipulative. During the battle against Onslaught, the X-Men found Xavier's files, the "Xavier Protocols," which detail how to kill many of the characters should the need ever arise, such as if they went rogue. Also it was revealed that when Xavier realized that the Danger Room had become sentient, he kept it trapped and experimented on it for years, an act that Cyclops called "the oppression of a new life" and equated to humanity's treatment of mutants. Later still, a de-powered Xavier was forced to admit that he had sent a group of hastily trained young mutants to Krakoa to save the original X-Men, resulting in their deaths. Because one of the mutants was Cyclops' brother Vulcan, Xavier erased Cyclops' memory of the event. He further manipulated the rescue team of new X-Men by making them think the meaningless noises the island made were intelligible speech—evidence that the island was alive—to match the new memories he had given Cyclops.

Xavier had multiple secrets that he hid from the X-Men beyond the Xavier files, Krakoa, and Danger incidents. Since the inception of the X-Men, he created and maintained a network of mutant espionage agents to work in dealings that were too dubious for the public eye of the X-Men, even entrapping Mystique into helping him (even though she killed his dear friend, Moira MacTaggert). He had also been part of the secret Illuminati society responsible for shooting Bruce Banner into space. There is also the issue that plagues only the longest of long-time X-Men readers. Throughout the years it had been implied that Xavier had always known about mutants beyond those he chose to be his X-Men. He had admittedly hand-crafted who he picked to be his core team members. This has serious implications however. For instance, it can be implied that Xavier must have always known about "Morlock" mutants, those with severe physical mutations, yet out of the utility of public appeal chose young mutants that he gave a life of privilege (though accompanied with life-threatening missions). Xavier intentionally let some mutants be his vision in Westchester, while others lived lives of horror and daily prejudice on the streets of Manhattan and around the world. Additionally, after the events of M-Day, Xavier was nowhere to be found. Even though he knew that the X-Men were looking for him, that his ancestral home was invaded by Sentinels, and that his school and the mutant community at large were in a state of crisis. He explained that he hid in England during this time out of embarrassment over losing his abilities and his role he played in the House of M saga.