As an adult, I think you have to go into this movie knowing that both Burton and Depp are big fans of the original Dark Shadows series. This movie stems from their love of the original. It really seems to be more of an homage to the television show than a serious movie. Prepare to suspend your disbelief on this one. The central love story really isn't well developed, which detracts from the plot. However, if you love the quirkiness that is the standard bill of fare for Burton/Depp collaborations, then you'll enjoy this movie.
As far as children go, I disagree with the 13+ recommendation. During a scene between Barnabas and Angie, there is a shot of Barnabas climbing in between Angie's legs as seen from her perspective. I really felt that was too risque for anyone younger than older teens.
The bottom line? See this movie if you love Burton, Depp, or Helena Bonham-Carter at their quirkiest. But leave the kids at home.