This is the book everybody gets in differentiation and integration in R^n, and it's a pretty good one, although the integration chapters are hard to read--maybe it was just my first encounter with exterior algebra that made it hard. As usual for Spivak books, clear exposition and lots of nice exercises. Unfortunately this one is old enough to be annoyingly typeset.
[Pete Clark] I don't really like this book, and I'm a big fan of Spivak in general. Does anybody else think that this rigorous multivariable Riemann integral theory is a dinosaur? And when Spivak starts talking about chains (in chapter four, I think), I don't know what the hell he's talking about. Presumably you could ignore that chapter and use the book as an introduction to differential forms. I can't suggest a substitute at the moment, other than Spivak's Comprehensive introduction volume 1, which is a wonderful book but which I still wouldn't want to read as a first introduction to forms. Come to think of it, I love forms to death, but maybe they're just plain confusing the first time around...
This skinny yellow book has replaced Munkres's Analysis on manifolds MR 92d:58001 as the text for 274, and I'm not sure it's an improvement. It's more like a modernized Calculus on manifolds. I haven't done more than glance through it, but the notation is reputedly horrible, and Spivak is definitely a superior expositor.