Rejection was a condition in which one's immune system fought against foreign tissue that had been transplanted into one's body. Cervaline was one drug which could help stave off rejection. (VOY: "Lifesigns")
In 2152, Doctor Phlox altered the DNA of a Calrissian chameleon's pituitary gland in order to make it a suitable replacement for Porthos' gland. The alterations were successful, as Phlox reported no signs of rejection later. (ENT: "A Night in Sickbay")
In 2368, Worf showed no initial signs of rejection after having a new section of spinal cord grown from his own tissue implanted in him. His condition deteriorated shortly after, leading to his death. However, due to the Klingon redundancies in his system, he revived shortly after. (TNG: "Ethics")
Rejection could also be a factor in the connection between a Trill host and symbiont was lost. It was measured by a drop in isoboramine levels, with levels below 40% of normal being harmful or fatal to the host and symbiont. During rejection, the symbiont had to be removed from the host to prevent it from dying, sacrificing the host in the process.
In 2371, Jadzia Dax experienced a series of suppressed memories (initially believed to be hallucinations), which caused her isoboramine levels to decline rapidly. Although the Symbiosis Commission attempted to stabilize the connection, Jadzia's condition deteriorated as her body began to reject the Dax symbiont. Jadzia was saved from rejection when the suppressed memories were brought to the surface and reintegrated with the rest of Dax's memories. (DS9: "Equilibrium")
Rejection could occur when a symbiont was implanted into a non-Trill host. In 2367, the host of the symbiont Odan was injured from an attack on the shuttlecraft he was traveling on; the injuries were severe, and required the removal of Odan. He could not survive outside a host for more than a few hours and a suitable Trill host was at least forty hours away, so William T. Riker voluteered to serve as a temporary host. However, Riker's body began to reject Odan, and Odan insisted that he be removed before he caused permanent damage to Riker. Ultimately, Odan was placed in a new host, and Riker was unharmed. (TNG: "The Host")