Computational

Computational Projects in Number Theory - Interesting problems, usually requiring extensive verifications or enumerations, to occupy the idle CPU time of workstations and personal computers. Compiled by Tomás Oliveira e Silva.
http://www.ieeta.pt/~tos/hobbies.html

Visible Euclidean Algorithm - Enter two positive integers, and click the button to see the operations of the Euclidean Algorithm.
http://www.math.umn.edu/~garrett/crypto/a01/Euclid.html

Basics of Computational Number Theory - Notes and Javascript illustrations by Robert Campbell.
http://www.math.umbc.edu/~campbell/NumbThy/Class/BasicNumbThy.html

Algorithm Design Manual - Number Theoretic Algorithms - A chapter from "The Algorithm Design Manual" by Steven S. Skiena.
http://www.cs.sunysb.edu/~algorith/major_section/1.2.shtml

LLL Page - Maintained by Keith Matthews. Papers, examples, pseudocode.
http://www.numbertheory.org/lll.html

Algorithmic Number Theory - Notes by Al Sethuraman.
http://www.csun.edu/~asethura/notes.html

Implementations of Extended LLL - Links and notes by Wilberd van der Kallen.
http://www.math.uu.nl/people/vdkallen/lllimplementations.html

The LLL Algorithm - Papers on the LLL algorithm and its applications collected by François Koeune.
http://www.dice.ucl.ac.be/~fkoeune/LLL.html

Future Directions in Algorithmic Number Theory - Some of the conjectures and open problems motivated by the "PRIMES is in P" papers, compiled at the AIM.
http://aimath.org/WWN/primesinp/

Computational Number Theory - Lecture notes by Robert Campbell, December 1997.
http://www.math.umbc.edu/~campbell/NumbThy/Class/

Some Number Records - Connected with divisibility and factoring.
http://www.loria.fr/~zimmerma/records/

Suggested Readings in Algorithmic Number Theory - Provided by the organizers of the MSRI Fall 2000 research program.
http://www.msri.org/local/library/reading_lists/0001-ant.html