My favourite has always been [*Introduction to Analysis* by Edward Gaughan][1]. I just found out the AMS published the [5th edition][2]. It contains, besides the standard calculus theorems, a very nice introduction to topology of the real line through the study of continuous functions.

I can say that reading this book as a text in my undergrad course largely contributed to myself becoming an analyst.


  [1]: http://books.google.com.mx/books?id=CSeSt8U-y10C
  [2]: http://www.ams.org/bookstore-getitem/item=amstext-1