Keisler's "Calculus: An Approach Using Infinitesimals" is a very cool freshman calc book using NSA. It dates back to 1976, and is available for free online: http://www.math.wisc.edu/~keisler/calc.html . Although I'm not aware of anyone who's using Keisler in the classroom today, it's under a Creative Commons license, and there is a newer book by Guichard and Koblitz that incorporates a bunch of material from Keisler: http://www.whitman.edu/mathematics/multivariable/ . In the world of the digital commons, it's a little hard to define how old a book is. It's like asking how old a bacterium is. Bacteria are in some sense immortal. They just evolve.
Another wonderful old calc book that is still in print is Calculus Made Easy, by Silvanus Thompson, 1910.
I noticed that another answer to this question got heavily downvoted for referring to a book published in the 1980's. The question was: 'What are the oldest books regularly used in your field (and which don't feel "outdated")?' It didn't specify what "used" meant -- used in research, teaching, personal study, ...? The lower you get on the educational totem pole, the shorter the half-life of a book. Someone posted that they liked Disquisitiones Arithmeticae, but that doesn't mean it's being used for teaching number theory to undergrad math majors. For freshman calc, it is extremely unusual for anybody to use anything more than 5 years old. The community college where I teach has an explicit rule forbidding the use of books of more than about that age.