To the best of my knowledge, there is one Saint Seiya series and four Saint Seiya Movies. This section will give a general idea of the story in Saint Seiya but I don't think this part can really be considered a spoiler since I will not divulge each episode's plot nor the various subplots and character histories. Kurumada created believable characters, each with a past and his or her own story to tell. These subplots and histories are very interesting and helpful in understanding each character in the anime.
I like to segregate the series into three parts -- Sanctuary, Asgard and Poseidon. In Sanctuary, Athena's enemy is Ares, the Greek God of War. The gods are suppose to be reincarnated as children, but Ares cheated by taking over an adult body. He skillfully turns Athena's guardians, the Gold Saints of Sanctuary (representing the 12 zodiac signs) against her. But Saori-san has one Gold Cloth (the Sagitarrius Cloth) in her possesion. Seiya and the other Bronze Saints must protect Athena and the Sagitarrius Cloth from Ares and his minions at all cost or Ares will rule the world.
Asgard takes us into the realm of Norse Mythology. Asgard has fallen into chaos and darkness under the leadership of Hilda. The only way for Seiya and the others to stop her and her evil plans is to collect the seven stones of Odin's crown. But each stone is protected by a God Warrior loyal only to Hilda.
Finally, in Poseidon, the Greek God Poseidon -- ruler of Atlantis and all the oceans and seas -- has been released from his imprisonment and has bonded with a young man. He kidnaps Athena and plans to submerge the whole earth and thus become its ruler. Seiya, Shiryu, Hyoga, Shun and Ikki enter Atlantis and face Poseidon and his Marine Shoguns (Sea Warriors) both to save Athena and the world.
Eris, the Goddess of Discourse, has found her chance to escape from her imprisonment in the golden apple. She plans to establish her rule on Earth but for that to happen she must erase Athena's existence. Athena's Bronze Saints come to her rescue but Eris has awaken her own loyal Saints, the Ghost Five, to fight Seiya and the others.
Hyoga came upon a man being betten by a group of men. He rescued the victim who said but one word to him -- Asgard. Hyoga leaves Sanctuary to go to Asgard to see what is happening there. Days pass and Hyoga hasn't returned to Sanctuary nor is there news of his whereabouts. Saori-san and her Saints visit Asgard in the hopes that Odin will know where Hyoga is. But Odin has his own plans for Athena and Sanctuary.