Popular books on algorithms

Two books by David Harel (Weizmann Institute). Very nicely written, suitable for anyone from late high school to graduate student and beyond. Each gives the big picture very clearly.
Computers Ltd.: What They Really Can’t Do (Oxford University Press, 2000. Revised paperback edition, 2003.)
Algorithmics: The Spirit of Computing (Addison-Wesley, 3rd edition 2004)

Textbooks and reference material

Wikipedia article Algorithm
Steven Skiena’s Stony Brook Algorithm Repository
The Dictionary of Algorithms and Data Structures

Popular articles

Two interesting recent articles by Bernard Chazelle (Princeton University) on the future of algorithms. Probably most suitable for undergraduates or advanced high school students.

Algorithm animations

A large collection of animated algorithms is available here