Cetus / The Whale Serpent
The dragon Cetus was slain by Perseus in the stories of the Greeks and Romans. This story was immortalized in the stars. There, you can find Cetus, his slayer Perseus, Andromeda, King Cepheus, and Queen Cassiopeia. 
Cetus, as a constellation, is sometimes also referred to as "the whale" or "the sea monster."  The constellation's abbreviation is 'Cet.' It is the fourth largest constellation in the sky, consisting of twenty-two stars, named in the time of Ptolemy, making it an ancient constellation as well.  It is also a faint constellation in viewing. 
Despite its constant connection to the whale, there is not much whale-like about the general description of Cetus, save for the enormous size, as his tail curls, serpent like, and his body is covered in scales. 
The ancient Mesopotamian grounds, namely of Sumer and Babylon, referred to this set of stars as Tiamat, the Bitter Waters, who represented the chaotic primal forces of the world. Marduk, the most powerful god of the Babylon, slew her and cut her in two. He made the sky from one half of her body, and the earth from the other half. After he had created a great many other things, he fastened the dome of the sky into place, using the North Star, and around it he set a dragon, with the likeness of Tiamat, to guard it for all time. 
Draco / The Dragon
The Constellation Draco has been associated to many dragons, mainly from Greek or Roman heritage. The Greek god Zeus led the other gods against the titans. Athena, goddess of wisdom, was said to have seized the tail of the Titanic dragon and thrown him into the void; thus, Draco was created. 
Interestingly enough, the head of Draco lies under the foot of Heracles, who was not unknown to slay dragons.  In some accounts, Draco is associated with the dragon Ladon, whose hundred heads remained eternally vigilant of the sacred golden apples in the Garden of Hesperides. This is because the constellation is circumpolar in the Northern Hemisphere, meaning that it never sets and remains visible over the horizon to those in the Northern Hemisphere. 
Draco was also related to the serpent in the Garden of Eden. When the Christian God created the world, it was a paradise; however, the two humans were warned that, while they could eat from any tree in the garden, they could not each from the Tree of Forbidden Knowledge. A serpent arrived, tempted them to eat it, and they did. Later, this same serpent was said to be the constellation Draco. 
During ancient times, over 4,000 years ago, the axis of the Earth pointed at the star Thuban, meaning serpent's head, which is the Alpha star of Draco's constellation.  Currently, the axis is pointing at the star Polaris, making it the current pole star.  The Earth's axis will not point to Thuban again for another 22,000 years. 
Water-Serpent / The Hydra
Of all the eighty-eight constellations, Hydra is the largest, stretching over one-fourth of the celestial equator.  There are two stories associated with this constellation from the Greek/Roman pantheon.
In the first story, the hero Hercules slew the Lernean Hydra.  The battle lasted for thirty nights, according to some accounts, and when he finally bested the monster, his father Zeus decided to cast the story in the stars, putting Hercules and his club in one constellation. The Water-Serpent, the Hydra, he placed near to the Lion. 
Two constellations are near Hydra's tail, Corvus (the Crow) and Crater (the Cup), which relate to the second story of this constellation.  In the second story, the god Apollo sent a crow to fetch water from a spring with a cup. On the way, the crow stopped at a promising fig tree, waiting several days for the fruit to ripen. When they did, the bird feasted luxuriously on the figs. Knowing Apollo would erupt in rage should he know the truth of the delay, the crow snatched up a water serpent and brought the serpent to Apollo, explaining that the serpent caused the delay.