Basilisk at its core is basically just a ninja adaptation of Romeo and Juliet. Thus when it comes to the plot of the anime, I doubt that any of it will seem significantly fresh or too unpredictable. If you are able to get past the unoriginal storyline, however, I think that there is still a lot to like about Basilisk.
The story moves at good pace: fast enough to prevent any dull moments; but takes time to develop the plot. As this is an anime about ninja, there is plenty of the action and fight sequences that one may expect from a series from this genre. I definitely feel my favorite part of the anime was probably the abundance of interesting characters. Although there were probably too many to fully develop, I thought that most of the Iga and Kouga ninja interesting and not too one-dimensional (except for the ones that die too early in the series).
There were numerous things that I disliked about the anime. My biggest gripe is the gratuitous amount of nudity and violence. A lot of the time I found the blood and boobs a bit unnecessary, taking away a lot of the poignancy of certain scenes. My other complaint is the lack of elaboration on the sub-story of Oboro and Gennosuke. Other viewers seemed to find the underlying love story interesting but I found it a bit too underdeveloped.
All-in-all, I liked Basilisk and would recommend the the anime to anyone looking for an action-packed, fan-service-filled, animated romp. The art is beautiful, the characters great and the plot not horrible. The story is definitely not a feel good anime, so anyone looking to find a happy-go-lucky series should probably look somewhere else. For all others, try a few episodes and see how you like it.