You probably know Cerberus, of Greek fame:
CE′RBERUS (Kerberos), the many-headed dog that guarded the entrance of Hades, is mentioned as early as the Homeric poems, but simply as “the dog,” and without the name of Cerberus. (Il. viii. 368, Od. xi. 623.) Hesiod, who is the first that gives his name and origin, calls him (Theog. 311) fifty-headed and a son of Typhaon and Echidna. Later writers describe him as a monster with only three heads, with the tail of a serpent and a mane consisting of the heads of various snakes. (Apollod. ii. 5. § 12; Eurip. Here. fur. 24, 611; Virg. Aen. vi. 417; Ov. Met. iv. 449.) Some poets again call him many-headed or hundred-headed. (Horat. Carm. ii. 13. 34; Tzetz. ad Lycoph. 678; Senec. Here. fur. 784.) The place where Cerberus kept watch was according to some at the mouth of the Acheron, and according to others at the gates of Hades, into which he admitted the shades, but never let them out again.
The monstrous hound Garm guards the entrance to Helheim, the Norse realm of the dead. It has four eyes and a chest drenched with blood, and lives in Gnipa-cave. Anyone who had given bread to the poor could appease him with Hel cake. On the day of Ragnarok, Garm will join the giants in their fight against the gods. The god of war Tyr will kill it in this cataclysmic battle but will die from the wounds inflicted by the hound.
It’s said a golden dog was set to guard the infant Zeus, and became the constellation Canis Major:
KUON KHRYSEOS was a golden dog set by Rhea to guard the infant god Zeus and his nurse the she-goat Amaltheia. Some say he was the same as Lailaps, the hound which Zeus first presented to Europa on Krete, and from her was passed on to King Minos, Prokris, Kephalos and Pandareos, before being placed amongst the stars as the Constellation Canis Major.
And of course we know what Artemis did to human stalkers:
“To Autonoe and Aristaios was born a son Aktaion, who was reared by Kheiron and trained as a huntsman, but was later eaten up on Kithairon by his own dogs [because] … he saw Artemis bathing. They say that the goddess changed him on the spot into a deer, and drove his fifty hunting dogs into a frenzy so that they unintentionally ate him. When he was no more, they looked for their master with great howls and bays, coming in the course of their search to Kheiron’s cave. He made a likeness of Aktaion, which assuaged their grief.” – Apollodorus, The Library 3.30
Here’s a book on dogs in art and myth that looks worth a read:
Dogs: History, Myth, Art by Catherine Johns