Here are some pieces of software that could enable interactivity in the notebook. Much of this software is java-based.
Geometry
See http://www.mathsnet.net/dynamic/index.html for an old survey of software.
http://www.dynamicgeometry.com/javasketchpad/ The java sketchpad, which is a java counterpart to Geometer's sketchpad. The input files look fairly easy to generate programmatically, so we could generate a file and then call the applet from the notebook, like the current jmol graphics work. The applet is free for non-commercial use.
GeoNext: http://geonext.uni-bayreuth.de/index.php?id=1917 is a GPL interactive geometry Java program. The last release was in mid-2007, so it seems fairly current.
Geogebra: http://www.geogebra.org/cms/ is a java program. The source is GPL, the documentation and translations are not. This has successfully been embedded in a Sage notebook.
See http://www.ct4me.net/math_manipulatives.htm#Manipulatives for more software.
Form controls for variables
Trac ticket #1322 ([http://trac.sagemath.org/sage_trac/ticket/1322]) has the beginnings of a manipulate command. See the manipulate.patch file and the examples at the end of the ticket.