Shapeshifter is a generic and generalized term applied to lifeforms that alter their form to assume various different appearances. The degree of physical transformation varies between different species. Some humanoid shapeshifters assume a different humanoid shape at the cellular level, while others can shift from non-humanoid to humanoid as well. Some project their various shapes as an illusion or telepathic manipulation and never physically change. Some lifeforms are non-corporeal and can manifest in different physical forms. Some shapeshifters need the aid of technology to assume other shapes.
Humanoid shapeshifters
Garth of Izar shapeshifted to appear as another James T. Kirk
Sulibans like Sarin with shapeshifting genetic enhancements had the ability to assume different humanoid appearances. (ENT: "Broken Bow") Humans who were taught to how to use cellular metamorphosis had the ability to assume the shape of other humanoids at the cellular level. Garth of Izar was taught this ability by Antos natives who also possessed it. (TOS: "Whom Gods Destroy")
The Devidian and the Quantum singularity lifeforms had the ability to assume various humanoid appearances. (TNG: "Time's Arrow, Part II", "Timescape") Satarrans also had the ability to appear as other humanoids. (TNG: "Conundrum")
Chameloids had the ability to change gender and appearance into humanoid forms of various sizes. (Star Trek VI: The Undiscovered Country) Dee'Ahn's species used shapeshifting to appear as different species and other genders. (ENT: "Two Days and Two Nights") The DNA thief lifeform also had this ability, but it needed to swap DNAs and appearances with the other humanoid it was shifting into. (VOY: "Vis à Vis")
Talosians and the M-113 creatures used telepathy to read the minds of others and to project the illusion of their appearance as different humanoid forms. (TOS: "The Cage", "The Man Trap") The unknown aliens who abducted Captain Jean-Luc Picard in 2366 had the ability to replicate and assume different humanoid appearances using advanced transporter technology. (TNG: "Allegiance") Iyaarans used a small device to assume the shape of other humanoids of other genders. (TNG: "Liaisons")
Non-humanoid shifters
A Wraith in its natural form
Changelings linking and shifting from solid to liquid
The Wraith and the Vendorians were non-humanoid lifeforms that could assume various appearances. While the Wraith used telepathy to search for shapes they turned into from the minds of others, Vendorians obtained this information through touch. They absorbed the memories and personality traits of the individual whose shape they were using. (ENT: "Rogue Planet"; TAS: "The Survivor") Rigelian hypnoid were simpler lifeforms and only projected the illusion of appearing as other lifeforms. (TAS: "Mudd's Passion")
Kelvans in their natural form had hundred tentacle-like limbs. Species 8472 were a non-humanoid tripedal species. Both were biologically capable of assuming various humanoid shapes. (TOS: "By Any Other Name"; VOY: "In the Flesh") The Ophidians could appear as an inanimate object of the same size. (TNG: "Time's Arrow, Part II") The Ornithoid lifeforms used a transmuter to assume larger humanoid and animal shapes. (TOS: "Catspaw")
The Changelings, also known as the Founders of the Dominion, were a liquid lifeform in their natural state. They had the ability to use their morphogenic enzymes to appear as various solid lifeforms or even as fire, fog, inanimate objects, flowers, trees and various small animals. (DS9: "The Search, Part II", "Things Past", "Chimera")
The Silver Blood are a liquid deuterium lifeform in their natural state and had the ability to change into anything they came into physical contact with, be it biological or technological. Coalescent organisms had the ability to mimic lifeforms in a similar way. Both also absorbed the memories of those they were shifting into. (VOY: "Demon"; TNG: "Aquiel") The Nacene were sporocystian lifeforms of energetic gelatinous liquid in their natural form, and had the ability to shift into various solid humanoid forms. (VOY: "Caretaker") Armus had a limited ability to shift between liquid and a solid forms. (TNG: "Skin of Evil")
The spaceborne entity and Gomtuu were living starships that could change to the needs of their crew. While the spaceborne entities changed their shape by transforming between energy to matter, Gomtuu only had an amorphous interior, capable of for example growing furniture and equipment from its walls and floors to suit the needs of its crew. (TNG: "Encounter at Farpoint", "Tin Man")
Non-corporeal to physical shifters
Many non-corporeal lifeforms had a physical form as well, (TOS: "Wolf in the Fold") but some had the ability to choose from various forms in which they wished to manifest. The Q (TNG: "Encounter at Farpoint"), the aliens who appeared as Rumpelstiltskin and Buck Bokai, (DS9: "If Wishes Were Horses"), the Koinonian energy lifeforms, (TNG: "The Bonding") the Douwd, (TNG: "The Survivors") the FGC 47 lifeform (TNG: "Imaginary Friend") were among these. They also had the ability to read the minds of others at some level.
The creature who called itself God, (Star Trek V: The Final Frontier) and the anaphasic lifeform were less capable of telepathy but could manifest in physical forms to fool other lifeforms. (TNG: "Sub Rosa") Allasomorphs were creatures of light in their natural form, but could appear as several humanoid and animal forms. (TNG: "The Dauphin") One non-corporeal lifeform used humanoids to experience various physical forms by making a corporeal subject pregnant and rapidly living through the childhood of the species. Upon death it returned back to its non-corporeal state. One such creature made Deanna Troi pregnant and lived a brief physical life as her son Ian Troi in 2365. (TNG: "The Child")