Pretty clearly, there isn't going to be a straight yes-or-no answer to the technical question "are vampires dead". Dictionary definitions -- or biological criteria -- don't get us very far, because the Cullens straddle the familiar distinction between dead and alive in all sorts of ways -- like viruses, as Heart Song wrote in another discussion a while ago. In a way, it's a mistake to ask the question at all. But failed questions often lead us to ask interesting new ones. As Ouisa says, "The Cullens challenge us to redefine the ordinary (and our selves)." Vampires' ambiguous status between life and death does get us to think about what it means to be alive.
Cocoa pointed out that the answer you give to the question will partly depend on why you are asking it. I'll go further and say that the question depends on why you are asking it. What exactly do we want to know when we ask "are vampires dead?" There are lots of different questions this could really be.
For what it's worth, the question I was mulling over when I posed the topic wasn't so much how we categorize vampires -- though that's an interesting question -- as what exactly it would mean for Bella to stop being human and become a vampire. Maybe the question I really wanted to ask wasn't "are vampires dead?" but "is becoming a vampire dying?" In one sense these are obviously equivalent, but the different emphasis affects how we look at the question -- which aspects of vampires' lives matter most to the answer. (So the fact that they don't have to breathe is maybe less important. The fact that they go through eternity in a kind of stasis, more or less frozen as they were at the time of changing, is more important).
So to put the question another way: Just how far does Stephenie want us to think of Bella's becoming a vampire for Edward as giving up her life for him? Not just in the way someone gives up their old life if they marry a foreigner and move to his native country. Not even in the sci-fi/fantasy sense of being changed into a different species. In the literal sense of, well, dying. Obviously, she's not dead in the way that Juliet ends up dead -- and we've been given a good look at that plot possibility in NM for contrast. Giving up her life for Edward will mean gaining a life with Edward in a much more concrete sense than Romeo and Juliet could ever hope to be reunited in some shadowy afterlife. This is not like Edward telling Bella in NM that when her natural life came to an end "I'll follow after as soon as I can." There's an obvious difference between being undead, living dead, vampire-dead (or whatever you might call it), and being REALLY dead. After all, as lots of people have pointed out, vampires must in some sense be alive, because they can be killed. And yes, they think and feel and walk and love and laugh and play baseball and generally seem to, well, have a life.
BUT....even though vampires share all this with the living, you might still look at their existence as something less than life, some kind of limbo state after life has ended. Something closer to ghosts or spirits or even zombies (since they have corporeal bodies) than just another alien life-form. There are lots of different concepts of ghosts (just like there are lots of concepts of vampires), but whatever else they are, ghosts are not really alive. Not like the living are. Because they have ceased to grow and change. Because they are cut off from a proper life among the living, even if (as in many ghost stories) they can still interact with them to some extent. Because they have left behind all the bodily processes and pleasures that situate us in the physical world: eating and drinking and sleeping and weeping, feeling fatigue and pain, aging and dying (except if their unnatural existence is brought to an end by special means). Because they have ceased to be embedded in the flow of time.
In this sense, it's not so silly to talk about BD (potentially) ending up a story about "two dead teens" (in Visitor's memorable phrase), even though they will in one sense be very much alive and together. And the effect of looking at vampires more like shades of the living is to make Bella's choice to be with Edward a much more somber one. It makes a Happy Ever After as an immortal vampire a more bittersweet ending. It makes clear the magnitude of the sacrifices Bella is willing to make for Edward -- this is not just about saying good bye to your parents and schoolfriends and the pleasure of chocolate chip cookies. And in sharpening our sense of this sacrifice, it shows us the depth of the impossible love that binds the two of them: "something so strong it could not exist in the rational world."
Stephenie dedicates Eclipse "to my children, Gabe, Seth, and Eli, for letting me experience the kind of love that people freely die for."
Does this tell us anything about how we're meant to understand Bella's choice?
adultae lexiconum recipientes nuntiis singulis