Tiling the plane and Packing problems.

The Discontinuous Groups of Rotation and Translation in the Plane by Xah Lee gives illustrations of the 17 different types of Wallpaper designs.
 
A Java Applet to play with Penrose tiles by Shuxiang Zeng is quite nice.

The Kali program at the Geometry Center is an applet that allows interaction with the frieze, wallpaper, and rosette groups.
 
Erich's Packing Center gives diagrams of the current best-known packings for 10 circles in a square, and other similar problems.  One excellent little problem as an example:  Fit 7 equilateral triangles with a side of 1 into a square with side 2.  YOu can find the answer at his site.