Favorite parts...

that are not action scenes?

The prologue- of Roman oppression, and Mary and Joseph's sojourn to Bethlehem
The Cave of Bethlehem
The Star of Bethlehem
The Nativity

Judah rescuing Esther's dove

The Roman soldiers breaking through the Hur Gates. The close-up of their violent faces always left an impression to me since my first viewing

Of course, its most famous non-action sequence- Ben-Hur's mother and sister having a reunion with the sleeping Judah.

Via Dolorosa- the revival of the dead child, the healing of the lepers, the reunion.

The collapse of the Roman House.

Throughout the film, there are a lot of memorable moments scattered around:
-The toddler son and his dog (poor kid...hope he's above two years old...)
-The crippled soldier surrounded by snakes.
-The prison guard torching his hand of infection.
-As Esther and the lepers leave the cave, a crippled beggar crawls to a pond.