Unfortunately, much of what we teach in "Calculus" and other courses is meaningless symbolic manipulation. There are many reasons for this:
The old calculus book by Toeplitz is one of the best ever written. It is also very short. Cauchy's calculus book is great. Euler's volumes on precalculus -- Introduction to the Analysis of the Infinite have never been surpassed. Unfortunately they fit into no standard modern course
Several calculus books are different because they are consitantly written by people that know and understand the engineering applications of Mathematics. The best of these is Gil Strang's Calculus .
Finally there are calculus books that have really taken the computer revolution seriously, and have thought very carefully about what it all means. Most of the "Computer Calculus" books are compleate junk. The best are superb. IMHO the best of the bunch is Calculus and Mathematica by Brown, Davis, Porta and Uhl.
There is, of course the famous Harvard Calculus project, by several well known and fine authors. While this is certainly in the right dirrection, the book is clearly not intended to be used at Engineering intitutes. I actually rather like much of the Harvard calculus, but I don't know of more than one or two of my colleges in Mathematics at Tech that would agree with me.
In may ways, the First Calculus Book Analyse des infiniment petits pour l'intellegence des lignes courbes by Guillaume Francois Antoine Marquis de L'Hopital is one of the best. (There is some controvery as to who the author was, see here for Johann Bernoulli's side of the story. )