The entry about Pascal's triangle on Mathworld leads to lots of other links.
http://mathworld.wolfram.com/PascalsTriangle.html
This page has LOTS of relevant number patterns in the triangle.
This applet will show large triangles
http://www.math.ohio-state.edu/~btk/Pascal/
A Java Applet that colors by divisors (Jeremy Baer at UW CSE).
http://www.cs.washington.edu/homes/jbaer/classes/blaise/blaise.html
Another applet at Simon Fraser
http://www.cecm.sfu.ca/cgi-bin/organics/pascalform
This link includes a downloadable program to simulate random walks
http://cps-www.bu.edu/ogaf/html/chp34lab1.htm
A Fractals Unit for Elementary and Middle School Students by Cynthia Lanius
http://math.rice.edu/~lanius/frac/
Math Forum unit on Pascal's triangle
http://mathforum.org/workshops/usi/pascal/pascal_intro.html
There is another triangle that can be used to compute the Bell numbers: