Of course, as we all know, the One True Calculus Book is
This is a book everyone should read. If you don't know calculus and have the time, read it and do all the exercises. Parts 1 and 2 are where I finally learned what a limit was, after three years of bad-calculus-book “explanations”. The whole thing is the most coherently envisioned and explained treatment of one-variable calculus I've seen (you can see throughout that Spivak has a vision of what he's trying to teach).
The book has flaws, of course. The exercises get a little monotonous because Spivak has a few tricks he likes to use repeatedly, and perhaps too few of them deal with applications (but you can find that kind of exercise in any book). Also, he sometimes avoids sophistication at the expense of clarity, as in the proofs of Three Hard Theorems in chapter 8 (where a lot of epsilon-pushing takes the place of the words “compact” and “connected”). Nevertheless, this is the best calculus book overall, and I've seen it do a wonderful job of brain rectification on many people.
[PC] Yes, it's good, although perhaps more of the affection comes from more advanced students who flip back through it? Most of my exposure to this book comes from tutoring and grading for 161, but I seriously believe that working as many problems as possible (it must be acknowledged that many of them are difficult for first year students, and a few of them are really hard!) is invaluable for developing the mathematical maturity and epsilonic technique that no math major should be without.
Other calculus books worthy of note, and why:
Spivak, The hitchhiker's guide to calculus
Just what the title says. I haven't read it, but a lot of 130s students love it.
Hardy, A course of pure mathematics
Courant, Differential and integral calculus
These two are for “culture”. They are classic treatments of the calculus, from back when a math book was rigorous, period. Hardy focuses more on conceptual elegance and development (beginning by building up R). Courant goes further into applications than is usual (including as much about Fourier analysis as you can do without Lebesgue integration). They're old, and old books are hard to read, but usually worth it. (Remember what Abel said about reading the masters and not the pupils!)
This is “the other” modern rigorous calculus text. Reads like an upper-level text: lemma-theorem-proof-corollary. Dry but comprehensive (the second volume includes multivariable calculus).