That depends on what you like in a vampire book. In the genre of supernatural romance or vampire romance there are a lot of great serieses, if you like that type (which I do). They're very different from Anne Rice. I would strongly recommend Christine Feehan's "Dark" series, and while you don't HAVE to read those in order, I would recommend you do, because little things in the books are clearer if you do. One recommended to me a lot are Laurell K. Hamilton's "Anita Blake Vampire Hunter" novels. It says she's a hunter, but she ends up with at least one as a romantic interest in the long run from what I've seen reading the blurbs about each book. I haven't had a chance to read those yet, but I have all of them in ebook form. They do have somewhat graphic (not gross graphic, but strong romance novel graphic) love scenes, so if you don't like that kind of thing you might not like these, but if you do, they're really good.

Incidentally Laurell K. Hamilton's "Merry Gentry" series is another good supernatural romance type, but not vampire.
Hmm...who else... Tanya Huff's "Blood Books" that the new series "Blood Ties" is based on is a good series so far, I've read the first two of five (there are short stories too in a 6th volume). Less romance in these, there still is some, but if you want something with less romance these are more like what you'd want, I think, but they're not solely about the vampire, he's just an integral character.
OH, and Katie McAlister writes vampire romance as well that I've enjoyed. Not as heavy and serious as Feehan's, Katie's are written in more of a lighthearted style. She has "Aisling Grey, Guardian" novels as well, and there's a bit of crossover between the two serieses, but you don't have to read the "Guardian" novels to enjoy her "Dark Ones" novels.
There's another I'm thinking of...I've only read one so far, called "Love Bites" but I've seen others by her I just haven't bought yet...let me check my bookcase here.... Lynsay Sands! That's the one....and another I've read two by so far that weren't bad, Amanda Ashley. She has a whole series too, but I haven't found them all yet.
Ok, reading this over I've come to the conclusion that I read WAAAAY too much! lol Probably the seven bookshelves double rowed with books could be considered an indicator too.

Anyway, Christine Feehan is easily my favorite of all of these, they're a good combo of story, suspense, hot romance, and each book leads well into the next, and the suspense really starts to build when you get towards the last two or three books (not including Dark Celebration, the very last so far, it's kind of a special christmas thing that lays off the suspense a bit and gets a bit funnier, but still has some important setups for future books and some bits of seriousness.) (oh, and including the three books that have short stories from the series in them, there are 16 books to this series so far, and I can't WAIT for the next!)