The Geertz definition is easily applied to Greek mythology. The definition starts with the system of symbols, which is in itself the system of gods. They are each represented by different objects (Hermes is often depicted with the winged helmet and shoes, Aphrodite on a shell with hearts.) The Greeks were famous for their statues of their dieties, perfectly proportioned to display the most physically fit definition of man. Here is am example from the museum at Delos;
The Greeks used their gods as a path to art and the creation of symbols. Often, Greeks also made sacrifices to their gods using the symbols prescribed to each issue at hand. When the weather was bad at sea, sailors were likely to pray and make sacrifices to Poseidon. They might even sacrifice a horse in his name, because of Poseidon's connection with horses and chariots (Hamilton, 26). Each problem in society had a different god to to combat it, and a different means of worshiping the problem away. Though individuals could pray at home or any time, going to temple was a social activity as well as a religious one. The Greeks are famous for their amazing architecture, visible in this ruin;
Different temples were assigned to different gods, this one being for Artemis, goddess of the woods and hunting. Religion existed for the ancient Greeks much like it does for Christians in a small farm town- they came together and used it as an opportunity to gossip and meet new people or old friends.
This system of symbols survives the second qualifier for religion as well, that it is long-lasting and pervasive. Though an extinct belief system, the mythology of the Greeks can be traced legitimately as far as 1000 BC, the best guess for when the Illiad was written (Hamilton, 16). There are sculptures of gods dating from around this time that continue well into the Roman empire, and are adapted throughout that culture as well. The system they established was concrete enough to apply to the Romans long after the descent of Greece. Nonbelievers throughout these periods were executed. Christians were placed in amphitheaters to fight lions and trained gladiators, simply because of their unwillingness to adopt this polytheistic view of the world. It is clear that this religion would not have survived if it had not been a convincing web a beliefs. It created an aura of factuality that lasted a long time, which makes it a legitimate religion under the definition provided by Geertz.