Here are the effects of each Godly Possession. You can toggle these on of off 
in the Items Menu AFTER BEATING THE GAME once you collect them. 
Warning: Equipping a Godly Possession disables Trophies.

Zeus' Eagle              - Infinite Rage of Sparta
Hades' Helm              - Max out Health, Magic and Item Meters
Helios' Shield           - Increase the Hits Counter by 3 times
Hermes' Coin             - Collect 10 time the amount of Red Orbs
Hercules' Shoulder Guard - Increase damage taken by a third
Poseidon's Conch Shell   - Infinite Magic
Aphrodite's Garter       - Continue to use Athena's Blades (the main weapon from the 
                           game's intro / while active, switch to another weapon to 
                           Combat Grapple)
Hephaestus' Ring         - Automatically win all Context Sensitive Attacks 
                           ("Quick Time Events") 
Daedalus' Schematics     - Infinite item use 
Hera's Chalice           - Causes the Health Meter to slowly drain over time, never 
                           completely emptying it.