To Kevin's excellent list I would add Guillemin and Pollack's very readable, very friendly introduction that still gets to the essential matters. Read "Malcolm's" review of it in Amazon, I agree with it completely.

Milnor's "Topology from the Differentiable Viewpoint" takes off in a slightly different direction BUT it's short, it's fantastic and it's Milnor (it was also the first book I ever purchased on Amazon!)