Marvin J. Greenberg and John R. Harper, Algebraic Topology, A First Course, Addison-Wesley, New York 1981.
Edwin Spanier, Algebraic Topology
Encyclopedic but rather dry.
P.J. Hilton and S. Wylie, Homology Theory
Engaging but marred by exotic terminology and notation.
H. Seifert and W. Threlfall, A Textbook in Topology
Still very useful for intuition and examples (trefoil knot complement, dodecahedral space, incidence matrices, etc.). The original German Lehrbuch der Topologie is also available.
William Massey Singular Homology Theory
Another standard text.