I suppose all writers have different definitions of what it means to be successful.
Some may not considered themselves successful until they earn incomes from their authorship as handsome as J.K. Rowling's, Nora Roberts's, Tom Clancey's or John Grisham's. Since mega-stardom in writing is rare, just as it is in acting or sports entertainment, such a lofty goal is extremely difficult to achieve--but certainly not impossible.
Others may consider themselves successful once a New York house publishes one of their books. This too is a lofty goal, though it is certainly more achievable than the one above.
Achieving publishing success through a small publishing house via e-book or print on demand may be the goal of a host of writers. If this goal is any easier to achieve than the New York house goal, it's only because there are many, many more publishers coming under this umbrella than under the one covering the more traditional publishers. Small or large, all publishers want quality work.
Many writers are independent thinkers, and some of these are independent authors. These folks, like independent film makers, might take the independent publication route. Once they publish their work in this way after they've striven to make it the best it can be, they will consider themselves successful.
To me, a book writer is successful once she completes her first novel or non-fiction project of book length--not when she publishes it, when she finishes it. Tons of people talk about writing a book "someday," few ever get it done. Why? Because writing a book, actually taking the time and effort to put down enough words to compose an entire book, is a huge, huge job. (And this doesn't count the research necessary before writing.) Unless a person has actually attempted a job like this, he has no idea how much work authoring a book is.
I say kudos to anyone who completes the task of writing the book and doesn't put off the job to be done "someday."
Fran Shaff, Award Winning Author