One thing I find very fun - and I think other fanfic people will, too - is that she borrows from all sorts of sources for situation, plot and character. She pulls from popular culture, classics, supernatural legends and melds it all together into a frothy vampiric Louisiana concoction. One large subplot is lifted intact from Dumas, for example. Of course that meant that I (and anyone who had read The Three Musketeers) knew how it would come out, but I found that just made it more fun.
Another thing Harris does well is to avoid the major pitfall of mystery novels of the Amateur Detective variety. I find with that genre the problem is that most people never come across one murder to solve, so it's hard to swallow when someone can't go to the store without stumbling over a dead body. The reader starts wondering why no one around this person thinks it strange that anywhere s/he goes people get murdered. Some authors solve the problem by having the main character become so good at solving mysteries that people seek him or her out when there's a murder the police can't solve. Others have the character go professional. Some just ignore the problem and hope the reader won't notice.
The problem is intensified with a small town setting, where several murders in a row would likely be noticed as unusual. But Harris deals with it well, both by the supernatural element (vampires live violent "lives" and so do the other supernatural creatures she introduces) and by varying the setting. Although the first book takes place solely in the small town in which Sookie lives, later books move to Dallas and New Orleans.
All told, I'm quite enjoying the books and think they make fun, escapist reading. The characters are witty and the dialogue (and Sookie's internal thoughts shared with the reader) are often LOL funny. The plots are clever (if often borrowed) and the characters become more real with each book.
There's another series of books by the same author that I think are also quite good, in a different way. These are the Harper Connelly mysteries. They have a supernatural element, but are much more tied to the real world.
Harper Connelly is a young women with a special power: she can detect the presence of dead people. She feels an emanation from corpses and can tell family or authorities where to look for a missing person (provided the person is actually dead). In the presence of a corpse she can also tell a little bit about the person - name, age, gender, how they died. She and her step-brother Tolliver go all over the country providing this service for a fee. Families and police departments are initially skeptical, but since she's always right they're often won over.
Harper and Tolliver are great characters, multi-layered and with a well fleshed out history. I've read three of the books so far and the mysteries themselves have all been predictable, but I didn't mind because I found the characters and plots compelling. The tone is much darker than the Sookie Stackhouse novels and the writing is better. I'm looking forward to getting the rest from the library.