I use Essential Topology, published by Springer. It's a very friendly book for an otherwise tersely written subject, though it lacks no rigour. The first 6 chapters are on general point set topology, and the remainder on algebraic topology.
Topology of surfaces, knots and manifolds is also recommended by my university, though I haven't read it properly I've had a glance in the library, and it seemed more basic, and focused (as the title implies anyway) much more on geometry. For me, Topology is more the study of continuous functions than geometry (especially since my first exposure was within an Analysis course!). The power of topology in geometry is entirely due to its powerful language to deal with continuity, which allows one methods to 'play with' shapes and surfaces, with topological invariants and the like to be analogous to geometric properties. Bear this in mind! for if, like me, you are intrigued and drawn in by strange geometry, then (if you haven't already seen it) you will undoubtedly be let down by the abstract definition of a topology which will seem to lead nowhere geometrical.