Firstly, the most well known classic of vampire novels is Dracula by Bram Stoker (1897). Stoker defined the modern vampire. It has been the basis for countless novels, films, and plays. It is the originator of the popularity of vampires today, and though Dracula is not as sexy as Lestat, it is none-the-less a necessary read for any vampire fan.
Another classic is Saint-Germain by Chelsea Quinn Yarbro (you can visit her website here). There are currently 27 books in the series, the first book is Blood Games (published 1979):
Yarbro has a huge fan following, her protagonist throughout the series Saint Germain is thousands of years old and has dedicated himself to saving damsels in distress. The novels follow his long life, from as early as the Roman times (68 BCE in the first novel) to 1977. Germain is a good-guy vampire, so he is similar to Louis in this respect, who regrets his vampiric necessities.
Another long-standing series and classic is Laurell K. Hamilton’s Anita Blake (you can visit her website here). There are currently 21 books in the series. The protagonist is Anita Blake, a vampire hunter. The first novel in the series is Guilty Pleasures (published in 1993):
While Anita Blake is a vampire hunter, she only kills those she deems evil, and befriends well behaved vampires (such as Jean Claude). Similar to Rice’s dark plots, themes and characters, Hamilton writes closer to horror than fantasy. These stories are also a lot more sexy than the other two mentioned, the later books sometimes seem more like erotica than straight horror, which makes Hamilton very similar to Rice.
Interview with the Vampire 