How to know when your character has 'legs' (enough to carry them forward)

We all know that readers love a good series - that moment of discovering a new character spanning several books, plenty of pages to sink get your teeth into. Bookshelves are full of iconic characters in literature, commercial and crime fiction who have sustained multiple outings, arguably becoming more of a focus than the story itself: Sherlock Holmes, George Smiley, Hercule Poirot, Miss Marple, Harry Potter, Inspector Morse, Kay Scarpetta and Vera Stanhope. The list goes on and on.

As a writer, and a voracious reader of some, I've often wondered if those authors set out to make their creations a common fixture, or whether the continued reappearance took the writers themselves by surprise, in the way some characters have a habit of stamping their authority on the page. In other words, how do you know if your character has 'legs' enough to trudge off the last page of one book... straight into the opener of another?