The best introduction to Calculus is classic "Calculus Made Easy" by Silvanus P. Thompson. It is in public domain, is a de-facto standard and is praised by many working scientists (Antony Zee, for example).
It gives you a working knowledge to get going with almost any practical problem you may encounter that needs to be approached with mahtematical analysis.
I would say that Spivak books are more about learning the culture of working mathematicians, and while with its merits one must be careful with commitment of investing her personal time to it.
Also, here is a great page to learn about good (and usually public) books for different branches of mathematics and physics by a Nobel-winning theoretical physicist G. t'Hooft
http://www.staff.science.uu.nl/~hooft101/theorist.html
Have not seen any of these public domain books yet, but I hope they catch on!
I don't have a favorite yet; Thomas was good, I expect to also like Stewart (which I am using for this first time this fall). As is typical, the math department as a whole chooses which book to use.
I'm not familiar with the `aristocratic' books (Spivak, Apostol), but I have heard they are excellent. I don't need to learn calculus anymore :) -- but I will check them out if I ever teach an honors class.
As a math prof, which texts(old or new) do you think are good? (fwiw I like Spivak)