Man, that's a question with more layers than a daylight ring. The original series by L.J. Smith is officially eight books: 'The Awakening', 'The Struggle', 'The Fury', 'Dark Reunion', 'The Return: Nightfall', 'The Return: Shadow Souls', 'The Return: Midnight', and 'The Salvation: Unseen'. That's the core.
Now, the rabbit hole goes deeper. After those eight, there are a bunch of continuation trilogies set in the same world, like the 'Stefan's Diaries' prequel books (six of those!) and the 'Hunters' trilogy. But the original story arc is those first four, then the 'Return' trilogy, capped with 'The Salvation'. I think the later ones, especially the 'Return' trilogy, get way less attention than the show, but they have their own weird, wild charm.
It's funny how the book universe kind of split off from the TV adaptation. The show obviously went in its own direction, so a lot of fans of the show have never even touched the eighth book, let alone the later spin-offs.
Honestly, 'Dark Reunion' feels like the real ending for the core four, everything after is a bit of a bonus round.