I will opine here a bit.
I want a vampire series that surprises me. Re-using the same tropes is okay, so long as it is done in an interesting spin. I want complex, interesting characters with compelling stories.
I want the vampires to make sense. For example, if a vampire kills every time he feeds and he feeds twice a week, then that one vampire makes a significant change in the murder rate of even a major, crime-ridden city. Likewise if one bite transforms someone into a vampire, then we'd quickly be up to our eyebrows in the things. You also have to explain how vampires are made, what their weaknesses really are--and it helps a lot if the overall "picture" is consistent.
Blood Ties actually approached this quite well. Vampires did not have to kill to feed, and few did. But territorial instincts were so great it was impractical for two vampires to dwell in the same city. No shape-shifting or flying. It wasn't that hard to kill a vampire, so staying covert made perfect sense.
Some adore the vampire-as-monster motif but ultimately that seems kinda boring to me. One important question to me for any vampire tale is--What happens to the person who changes? For example both Buffy and Bram Stoker's Dracula more-or-less came out and called vampirism a kind of demonic possession. The series Forever Knight strongly hinted that to become a vampire was to gain a whole new set of very strong instincts. On the other hand, why did vampires in Blade change personality so much? No idea. In The Strain this is explained in (horrifying) detail, one of the few examples of totally monstrous vampires that worked for me (their entire biology is reworked, including the loss of higher brain functions).
Methinks True Blood is an excellent example of a vampire t.v. series--not least because the vampires in question make total sense. They are diverse, and respond in an understandable way to their condition.
Mind you, I would also point out that as premises for series The Vampire Diaries is far better suited that Twilight. The former has actual adversaries in one way or another that stay around and interact. The bite is not a death sentence, unlike the latter, and the use of a long-term background lends itself to complex story arcs. What I don't like about the series is the relative lack-of-depth in the main characters, and in the fact that this particular high school seems made up of nothing but pretty people. Where, I ask, are the Willows and Jonathans and Xanders? Why is everyone a Cordelia or a Harmony? How dull! Ms. Myers' work outstrips the t.v. series in that at least (haven't read the books, so cannot judge them).