Simply put, this is the ability to see the future. Normally the image of the future is not too clear or specific, and can be impossible to interpret without other information. Sometimes this seen future can be changed.
[X-Files, Babylon 5]
This is the ability to get readings off of objects or places about their pasts. The subject takes an object and will be able to sense things about the person who used it or about any especially traumatic events that the object may have been associated with, such as being if the object were a murder weapon.
[X-files; Tomorrow People, and real life(?)]
Empathy is a lesser form of the mind reading aspect of Telepathy. It is the ability to sense emotions of other people, and in its stronger form, to project your emotions on other people.
[ST:TNG, others]
Image Projection is a form of Telepathy. Basically it is projecting images into other peoples minds so that they see things that are not there. The mind now believes the image is there and will compensate by adding the expected side effects of the thing being imaged, such as temperature, or seeing it on a radar screen. This same process can be used for sounds as well, however neither the image or any sounds can be recorded or photographed.
[Tomorrow People, Babylon 5]
Projection is the ability to project yourself out of your own body to take a look around without having to be there physically. Projection can also go into the past, other planets, or onto other planes of existence such as the astral plane. It could even be used to project into dreams.
[marvel comics; Babylon 5, Dreamscape, others]
This is mind over matter. The ability to bend objects, or if more powerful to move objects with the mind. If a finer form of control is developed it can be a deadly weapon.
[Babylon 5, Battlestar Galactica, Tomorrow People]
Telepathy is the ability to read minds or to project thoughts into another persons mind. This is normally a form of communication but depending on the power of the telepath, it can be a drastic method of mind control.
[Tomorrow People, Babylon 5, just about everything else.]
This is a form of mind over matter, that allows a person to either instantly relocate himself to another location, or to open a pathway through hyper space that allows them to hop from one location to another.
[Tomorrow People]
In areas where no one knows the language, the gifted person can read the meaning behind what a person is saying and their mind instantly translates it as if the other person had spoken a known language. This gift also works in reverse, when the gifted person speaks the other person hears it as if they had been spoken to in their native toung. This gift is very powerful and can extend the ability to any compainions the gifted person happens to be traveling with.
[Doctor Who; Tomorrow People]
This is the ability to see people's Auras, Angels, Ghosts and/or a connection to other planes of existence. If the ability is especially strong it can allow communication with those spirits or planes of existence.
[Ghost, The Sixth Sense, others.]
Thoughts can be recorded. This can be accomplished by electronically digitizing the brain, or by some more elusive method of recording telepathic communication.
[Babylon 5, Max Headroom.]
This is the equivalent of a grenade. If activated it lashes out, psychically attacking everyone within range, and sensitive enough to be vulnerable to it.
[Babylon 5 books]
When keyboards and vocal control over computers or ships appear to be too slow, the next step is thought controlled equipment.
[various B movies, ST:TNG]