Between Heather's post on first chapters and Janet's challenge regarding gripping first lines, I've been noticing first lines recently.
I was surprised to see that many of my favorite books begin with a first line that focuses on character, relationships, or theme, rather than on action.
Many start by setting up the voice of the narrator. Most of the Nero Wolfe books do this, beginning with Archie's voice, often relating something about the dynamics of the household or about his relationship with Wolfe. (For instance in Fer-de-lance Archie gripes about how is is often the one being sent on errands, in Prisoner's Base he relates his latest ploy to aggravate Wolfe into action, in The Rubber Band we see him hassling Wolfe...) One of the most enjoyable elements in Stout's books is the relationship between Wolfe and Archie, and in one way or another many of the books start with a focus on that relationship.
Another example of starting with the narrator's voice: Amelia Peabody in The Mummy Case:
"I never meant to marry. In my opinion, a woman born in the last half of the nineteenth century of the Christian era suffered from enough disadvantages without willfully embracing another."
Can't you just hear her?