C* Algebra textbook recommendation

W. Arveson: An Invitation to $C^*$-Algebras, Springer (The presentation is as simple and concrete.)

G.J. Murphy: $C^*$- Algebras and operator theory. Academic Press. (Very accessible and readable.)

K. Davidson: $C^*$-algebras by example. AMS. (Useful example-based approach.)

In addition to the other answers, I would also recommend :

1. Dixmier, C$^{\ast}$ algebras : It is old, and hard to come by, but really very informative. The treatment of Group C* algebras is particularly good (as it is in Ken Davidson's book)

2. R.G. Douglas, Banach Algebra Techniques in Operator Theory : A second edition of this has recently come out. The book focusses on applications to the theory of Fredholm and Toeplitz operators, so it is useful if you want to do some operator theory.

3. Gelfand, Raikov and Shilov, Commutative Normed Rings : Another very old book, but it was the first book (that I came across) on the subject, and it is really very cool. It contains Gelfand's famous proof of Weiner's theorem

4. Kadison and Ringrose, Fundamentals of the Theory of Operator Algebras : It is a 4-volume book that covers everything. The first volume contains, for instance, a C* algebraic proof of the Stone-Weierstrass theorem (which is due to De Branges, I believe).

Other somewhat more advanced books :

1. Takesaki, Theory of Operator Algebras

2. Pedersen, C$^{\ast}$ algebras and their Automorphism Groups

I really like C$^*$-Algebras by Example. Very readable intro on my opinion.