There are currently seven novels in the Southern Vampire series. The premise is simple: synthetic blood has allowed vampires to come out of hiding, since they no longer need human blood to survive. The series starts with quirky waitress Sookie Stackhouse meeting the first known vampire to inhabit her rural hometown of Bon Temps, Louisiana. Adventure, mystery, and romance ensue.
In addition to the novels, there are a handful of short stories available that are set in the Sookie Stackhouse universe.

Here is the complete list to date:

2001 - Dead Until Dark
2002 - Living Dead in Dallas
2003 - Club Dead
2004 - Dead to the World
2005 - Dead as a Doornail
2006 - Definitely Dead
2007 - All Together Dead
2008 - From Dead to Worse

The first 3 novels of the series (Dead Until Dark, Living Dead in Dallas, and Club Dead) are available in an anthology called Dead in Dixie for a very reasonable price. The 4th and 5th books (Dead to the World and Dead as a Doornail) are similarly available in the anthology Dead by Day.

 

The following include Southern Vampire short stories by Charlaine Harris:

2004 - Powers of Detection features the short story "Fairy Dust"
2004 - Night's Edge contains the novella "Dancers in the Dark"
2004 - Bite contains the short story "One Word Answer"
2006 - My Big Fat Supernatural Wedding contains the short story "Tacky"
2007 - The anthology Many Bloody Returns contains "Dracula Night"