Probably the first multi-volume work that I read was the Iliad, followed by the Odyssey. I learned that there was something immensely satisfying about holding a BIG book and committing to it. That was my initiation and it's all Homer's fault.
I know I've read many multi-volume works that I'd be ashamed to admit to, but there are also many excellent ones. Looking at my bookshelves, I see:
Robertson Davies --
The Deptford Trilogy
Lawrence Durrell --
The Alexandria Quartet
Robert Graves --
I, Claudius and
Claudius the God (ok, not quite a trilogy)
Winston Graham -- something like 8 or 9 Poldark novels
Colleen McCullough -- the series on the demise of the Roman republic that starts with
The First Man in Rome and ends with
The October Horse
Ellis Peters/Edith Pargeter -- Brother Cadfael mysteries and others
Dorothy Dunnett -- the Lymond series and the Niccolo series
and when I need a laugh, my guilty pleasure ~
Lindsey Davis -- the Falco detective series
looks like I'm addicted to 'em.