Hello @nbmiii

First of all the entire saga has 5 games, not 3. Secondly, yes…they are related in one way or another. Here is a small summary for each game and the order they were released.

God of War – was the first game from this series. It was released for PlayStation 2 on March 22, 2005 and shows the story of Kratos and how he was tricked by Ares. He killed his family and turned against the God of War.

God of War 2 – was also released for PlayStation 2 on March 13, 2007 and shows the story of the new God of War, which is Kratos. He killed Ares and now he is aiding the Spartan army. This angers some of the Gods from Olympus and the battles starts again.

God of War: Betrayal – was released for mobile phones, on June 20, 2007. The action takes place between the first and the second game and shows how Kratos is learning about the powers he has as a God of War.

God of War: Chains of Olympus – runs only on PlayStation Portable and is the 4th game. It was released on on March 4, 2008 and the action starts when Kratos was sent by the Gods to defend Attica.Kratos fights his way to Tartarus in this game.

God of War 3 – is the latest game from this series. It was released on March 16, 2010 for PlayStation 3 and in this game, Kratos’ seeks revenge against Zeus.

All the games are related and novel will be released in May. For more information about the God of War novel, please check these links:
http://www.randomhouse.com/catalog/display.pperl?isbn=9780345508676
http://playstation.joystiq.com/2009/07/13/del-ray-announces-first-god-of-war-novel-for-march-2010/
http://cache.gawker.com/assets/images/kotaku/2009/07/gowbook.gif

It is probably one of the best video game series I have even played, in terms of storyline connection. God of War I, II, and III are put together seamlessly. Any gaps that were in GoW I are filled in by GoW II and the same for GoW III. I think God of War would make a really amazing book and movie, I would pay to see it at midnight. I think there would be a few things here and there that would need to be changed, but in total from the start of GoW I to the end of GoW III, The God of War Franchise is complete.

***POSSIBLE SPOILER ALERT***

http://www.youtube.com/watch?v=i9HU1rmxXH8
http://www.youtube.com/watch?v=To8-uyioJhs&feature=related&ajax=1&nocache=1270667568637
http://www.youtube.com/watch#!v=MrPAs_Knugg&feature=related

I consider the 3 main God of War games to be a very well thought out and continuous story but the handhelds seem more like stand alone adventures that while still connected, work just fine on their own.

(I haven't played the mobile version however)

Even though the three main episodes (on Playstation 2 and Playstation 3) follow each other pretty closely story-wise, especially God of War 3, which more or less starts where God of War 2 ended, I still can't avoid the feeling I'm playing the same story again. All three games cover part of the ten-year campaign of Kratos, and mostly focus on the last part, when he turns agains his former master(s), and goes on a rampage against the gods, I can't help to feel like I'm killing the same Gods over and over again. For instance, I'm battling Zeus both in God of War 2, and in God of War 3. Hades and Chronos keep returning in the storyline too, as does Aphordite, who appeared in the first God of War, and again makes a (tasteful!) appearance in God of War 3.

So, while the storyline probably is quite complete, the recurrence of bosses makes the whole event somewhat repetitive..