First of all I want to comment that beyond the two "standard textbooks" Andrew L. mentioned (Switzer and Whitehead), there is at least Adams's classic "Stable Homotopy and Generalised Homology", which goes in some aspects deeper than Switzer. Besides this, I want to mention two more recent books:

• Neisendorfer's Algebraic Methods in Unstable Homotopy Theory. It is perhaps not perfectly edited, but seems to essential reading as a source for modern unstable homotopy theory.
• Kochman's Bordism, Stable Homotopy and Adams Spectral Sequences. It deals pretty early with spectral sequences and proves some standard results in classical homotopy theory via them (like Blakers-Massey, Freudenthal..) In then goes on to introduce the stable category and compute the first 20 stable homotopy groups of the sphere (or so). It also treats characteristic classes and bordism. The treatment of the stable category is not really to my taste, but the book definitely deserves a look.