Signal processing textbook recommendations depend on many factors. For example, different signal processing textbooks cover different topics of interest and are appropriate for different backgrounds. The introductory level is served by books such as Signal Processing First (McClellan, Schafer and Yoder, Pearson/Prentice Hall 2003) and Signals and Systems, 2nd Ed., (Haykin and Van Veen, Wiley 2003. Of course this one is my favorite.) The text I use in my senior-level signal-processing class is Discrete-Time Signal Processing, 3rd Ed. (Oppenheim and Scafer, Prentice-Hall 2010). For topics in estimation and detection theory I often use Steven Kay's texts Statistical Signal Processing, Vol. 1, Estimation Theory (Kay, Prentice Hall 1993) and Vol. II, Detection Theory (Kay, Prentice Hall 1998). I also like Statistical Signal Processing: Detection, Estimation, and Time Series Analysis (Scharf, Addison-Wesley 1991).
Free signal-processing textbooks:
There are several "free" signal processing textbooks available on the web, including Introduction to Signal Processing by Orfandis and The Scientist and Engineer's Guide to Digital Signal Processing by Smith.