Diophantine m-tuples
Sets with the property that the product of any two distinct elements is one less than a square. Notes and bibliography by Andrej Dujella.
http://www.math.hr/~duje/dtuples.html

Diophantus Quadraticus
On-line Pell Equation solver by Michael Zuker.
http://www.bioinfo.rpi.edu/~zukerm/cgi-bin/dq.html

Egyptian Fractions
Lots of information about Egyptian fractions collected by David Eppstein.
http://www.ics.uci.edu/~eppstein/numth/egypt/

Hilbert's Tenth Problem
Given a Diophantine equation with any number of unknowns and with rational integer coefficients: devise a process, which could determine by a finite number of operations whether the equation is solvable in rational integers.
http://www.ltn.lv/~podnieks/gt4.html

Linear Diophantine Equations
A web tool for solving Diophantine equations of the form ax + by = c.
http://www.thoralf.uwaterloo.ca/htdocs/linear.html

Pell's Equation
Record solutions.
http://www.ieeta.pt/~tos/pell.html

Pythagorean Triples in JAVA
A JavaScript applet which reads a and gives integer solutions of a^2+b^2 = c^2.
http://www.hbnweb.de/pythagoras/pythagoras.html

Pythagorean Triplets
A Javascript calculator for pythagorean triplets.
http://www.faust.fr.bw.schule.de/mhb/pythagen.htm

Quadratic Diophantine Equation Solver
Dario Alpern's Java/JavaScript code that solves Diophantine equations of the form Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0 in two selectable modes: "solution only" and "step by step" (or "teach") mode. There is also a link to his
http://www.alpertron.com.ar/QUAD.HTM

Rational Triangles
Triangles in the Euclidean plane such that all three sides are rational. With tables of Heronian and Pythagorean triples.
http://grail.cba.csuohio.edu/~somos/rattri.html

The Erdos-Strauss Conjecture
The conjecture states that for any integer n > 1 there are integers a, b, and c with 4/n = 1/a + 1/b + 1/c, a > 0, b > 0, c > 0. The page establishes that the conjecture is true for all integers n, 1 < n <= 10^14. Tables and software by
http://math.uindy.edu/swett/esc.htm

Thue Equations
Definition of the problem and a list of special cases that have been solved, by Clemens Heuberger.
http://finanz.math.tu-graz.ac.at/~cheub/thue.html