If you look closely in the God of War Series, you can actually see that Kratos did not want to kill at least three people and here's the list.
3. Hercules (or Heracules)
Kratos actually did not want to kill his older brother, shown by him trying to reason with him. He also told Hercules that he shouldn't strive to be an Olympian, since their time was ending. But he killed him only because he joined the fight, not for personal reasons.
2. Hephestaus
At of all the Gods, Hephestaus was probably Kratos's second favorite. He enjoyed talking to him while in the UnderWorld, and was always asking him for help. Also, it seemed that Kratos and Hephestaus may had been friends judging by the way they talked to each other. If only Hephestaus hadn't tried to stop Kratos from killing Pandora... he still had a nice death do.
1. Athena
Athena is the number one person that Kratos did not mean to kill, and showed great regret upon doing so. When he met her in the Underworld, he seemed dearly sorry that he had impaled her. Also, she seemed to be the only god he would listen to, save Hephestaus. But he still chose the right thing in the end and gave humanity Hope, which really ticked Athena off.
And there's that. If you have any other people he didn't want to kill, you can add them.