Hybrid

A hybrid was a lifeform produced from the mating of parents of two different species or a mixture of DNA from two species. The Eighth Doctor claimed that two species were "hardly ever" able to interbreed, and "certainly not" when physiology was as different as the termite-like Kromon and the humanoid Eutermesans. (AUDIO: The Creed of the Kromon)

Impacts of hybridisation
Hybrids were not always healthy. Hybridisation was known to cause terrible mutations. (TV: Delta and the Bannermen) Some individuals were sterile and had shortened lifespans. (PROSE: The Scales of Injustice) Other hybrids were more successful. Flisk/human hybrids were better at reading the minds of humans than pure Flisk. (PROSE: Snowglobe 7)

General examples
Silurians and Sea Devils could create cross breeds, even though they were different species. Their hybrids were shunned by society, were sterile and had shorter lifespans due to cellular degeneration. (PROSE: The Scales of Injustice)

The Raxacoricofallapatorians and their relatives from their sister planet, the Abzorbalovians, sometimes bred together; the Abzorbalovian Rebels were descended from the Raxacoricofallapatorian Huspick Degenerate. (WC: Captain Jack's Monster Files: Slitheen)

In the 26th century, Githians couldn't marry outside their species since they had trouble maintaining the purity of their gene pool. (AUDIO: Phobos)

By the year 5,000,000,000, interbreeding and evolution had resulted in there being only one "pure" human left, Cassandra O'Brien.Δ17. She considered the rest of the current human race "mongrels". (TV: The End of the World)

Human hybrids
The Eighth Doctor once described himself as "half-human, on my mother's side". (TV: Doctor Who) One account suggested this was a ruse to fool the Master, involving the use of a Chameleon Arch (COMIC: The Forgotten), although the Twelfth Doctor later proclaimed "The hybrid destined to conquer Gallifrey and stand in its ruins is me." - though that could very well have been a reference to Ashildr who later referred to herself as "Me". (TV: Heaven Sent)

The Doctor's great-grandson, Alex Campbell, was half-human, being the child of Susan Foreman and David Campbell. (AUDIO: An Earthly Child) Gallifreyan genes constituted only 7% of his genome so he had no telepathic abilities and couldn't regenerate. (AUDIO: Relative Dimensions)

Although both Amy Pond and Rory Williams were human, their child, Melody Pond, contained Time Lord DNA as a result of her being conceived in a TARDIS that was travelling through the Time Vortex. (TV: A Good Man Goes to War)

Arnold Golightly was a human-Vespiform hybrid; he had a human mother and a Vespiform father. (TV: The Unicorn and the Wasp)

Melanie Baal was a Silurian-human hybrid from an alternate timeline. (PROSE: Spiral Scratch)

Gavin had a human mother and a father of an unknown species. (TV: The Empty Planet)

Adam Lloyd was the half-human son of Samuel Lloyd and Eve. (TV: The Mad Woman in the Attic)

Freda's mother and grandmother were both Ghosties, while the rest of her family were human. (AUDIO: Asylum)

Ku'ra Debrekseny was half human and half Flisk. (PROSE: Snowglobe 7)

Peter Summerfield was a human-Killoran hybrid; he had a human mother and a Killoran father. (PROSE: The Squire's Crystal)

One of Adelaide Brooke's descendants fell in love with a Tandonian Prince and created a new human-Tandonian hybrid species. (TV: The Waters of Mars)

King Peladon was a human-Peladonian hybrid; he had a human mother and a Peladonian father. (TV: The Curse of Peladon) He later had a three-quarter-Peladonian-quarter-human hybrid daughter, Thalira. (TV: The Monster of Peladon)

Josiah W. Dogbolter was a human-frog hybrid. (AUDIO: The Maltese Penguin)

Thomas Kincade Brannigan and Valerie Brannigan produced several Catkind-human hybrid children. They looked like kittens but could say words like "mama". (TV: Gridlock)

Tanya Webster was a genetically engineered human-Ice Warrior hybrid. (AUDIO: Red Dawn)

King Yrcanos and Peri Brown had 3 children, which would make their children Krontep-human hybrids. (AUDIO: Peri and the Piscon Paradox) Later on they also had 3 grandchildren who were three-quarter Krontep-quarter-human hybrids. (COMIC: The Age of Chaos)

Andred and his wife Leela conceived a son, which would make him a Time Lord-human hybrid. (PROSE: Lungbarrow)

Other species
Chukk was a Silurian/Sea Devil hybrid. (PROSE: The Scales of Injustice)

Kronos was an Eternal-Chronovore hybrid. (PROSE: The Quantum Archangel)

Jack was a Larian, with a little bit of Terian on his mother's side. (PROSE: Penny Wise, Pound Foolish)

Tactical Officer 25463 was a Weave/Tahnn hybrid. (PROSE: The Glamour Chase)

Shazar was a Time Lord hybrid. (COMIC: Return of the Daleks)

Hybrids produced by other means
When the Pyroviles tried to conquer Earth, they converted the Sibylline Sisterhood into human-Pyrovile hybrids. (TV: The Fires of Pompeii)

After the Doctor resurrected Ashildr using the Mire medical kit, Ashildr became human with "a little piece" of Mire technology inside her. According to the Twelfth Doctor, this meant that "in a way, she's a hybrid." (TV: The Girl Who Died) Sam Swift later became a hybrid of the same nature, created by the same means. (TV: The Woman Who Lived)

When the Tenth Doctor halted his regeneration by shifting his regeneration energy into his severed hand, a Meta-Crisis occurred, resulting in Donna Noble being turned into a Time Lord-human hybrid, giving her the Doctor's knowledge (although the Doctor later had to erase her memory lest she burn up). The Doctor's hand turned into a duplicate of the Doctor apart from having only one heart as opposed to two, being unable to regenerate and having the lifespan of a human. (TV: Journey's End)

In 1994 Alaska, the reviving Permians inadvertently used their bioelectric fields to fuse together the bodies of nearby wildlife (such as seals and walruses) into monstrous hybrids which attacked people out of pain and fear. Many of these were consumed by the Permians, and the rest died soon after the Permians did, as they required their energy to sustain them. (AUDIO: The Land of the Dead)

The Karfelon Megelen became a Karfelon-Morlox hybrid by way of a scientific accident involving Mustakozene-80 which fused his DNA with that of a Morlox creature. (TV: Timelash)

The Eutermesan L'da and the human Charlotte Pollard were genetically engineered into Kromon queens. (AUDIO: The Creed of the Kromon)

Davros attempted to transform some of his Daleks into Time Lord hybrids, intending to fulfil an ancient Gallifreyan prophecy which warned of a Dalek-Time Lord Hybrid that would conquer Gallifrey. (TV: The Witch's Familiar) However, the Twelfth Doctor later claimed that the Daleks would never allow anything to be "half Dalek" and that the hybrid of Time Lord prophecy was "Me". (TV: Heaven Sent)