An extensive study of the surviving literature will reveal that the gods were given certain animals as sacrifices. Without listing all of the source material, here I'd like to simply list the most common animals offered to the gods. Even if you do not practice animal sacrifice, you can use this list when deciding what type of food to prepare for particular festivals, etc.
Apollon- adult cow, adult goat, adult bull
Aphrodite- adult goat, kids (i.e. baby goats)
Artemis- adult goat
Asklepios- adult cow
Athena- adult cow, adult sheep
Demeter- adult pig, adult cow, young pig
Dionysos- adult cow, adult goat
Hera- adult cow, adult sheep
Hermes- adult sheep, ram
Kore / Persephone- ram, adult cow, young pig
Poseidon- adult sheep, ram
Zeus- adult cow, adult sheep, young pig
More info on the subject coming soon.