Here are some helpful scripts for Geometer's Sketchpad.
If you own a copy of Geometer's Sketchpad, you can download any of the .gsp files and use the scripts yourself.
Circle Tools Triangle Tools Polygon Tools Segment Tools Misc. Tools
Circle Tools 

CircleBy3Points  Given three points, construct a circle such that those three points are on the circle.  
CircleBy3Tangents  Given six points (two on each of three lines), construct a circle that is tangent to each of those three lines. In this case, no pair of the tangent lines can be parallel.  
CommonExternalTangent1 & CommonExternalTangent2 
Given the centers of two circles and points on them (in the order centerpointcenterpoint), construct a line which is tangent to both circles on the "outside," and construct the points of tangency. (1 constructs one of the common external tangents; 2 constructs the other)  
CommonInternalTangent1 & CommonInternalTangent2 
Given the centers of two circles and points on them (in the order centerpointcenterpoint), construct a line which is tangent to both circles on the "inside," and construct the points of tangency. (1 constructs one of the common internal tangents; 2 constructs the other)  
TangentCircleAtPoint  Given the centers of two circles and points on them (in the order centerpointcenterpoint), construct a circle which is tangent to both circles, and which is tangent to the first circle at a changeable point.  
TangentThroughPoint  Given the center of a circle, a point on the circle, and another point, construct a line tangent to the circle through the given point, and construct the point of tangency.  
Circle Tools
Triangle Tools
Polygon Tools
Segment Tools
Misc. Tools 

Triangle Tools 

Centroid  Given 3 vertices of a triangle, construct its medians and centroid.  
Circumcenter  Given 3 vertices of a triangle, construct its sides' perpendicular bisectors and its circumcenter.  
Circumcircle  Given 3 vertices of a triangle, construct its circumcircle
(the circle through the vertices, with the circumcenter as its center). (Note: This script is identical to the CircleThrough3Points script in Circle Tools) 

CircumOrthoIncentersCentroid  Given 3 vertices of a triangle, construct its circumcenter, orthocenter, incenter, and centroid.  
EulerLine  Given 3 vertices of a triangle, construct its Euler Line (through the centroid, circumcenter, and orthocenter).  
Incenter  Given 3 vertices of a triangle, construct its angle bisectors and incenter.  
Incircle  Given 3 vertices of a triangle, construct its incircle (the circle which touches each side, and has the incenter as its center).  
Isosceles  Given 2 points defining the base and a segment whose length is the desired length of the altitude, construct an isosceles triangle.  
MedialTriangle  Given 3 vertices of a triangle, construct its medial triangle.  
MidsegTriangle  Given 3 vertices of a triangle, construct its orthocenter, connect the vertices to the orthocenter, and create a triangle whose vertices are the midpoints of those segments.  
NinePointCircle  Given 3 vertices of a triangle, construct the circle
(and the center of the circle) which passes through: a) the feet of the three altitudes, b) the midpoints of each side, c) the midpoints of the segments connecting each vertex with the orthocenter. 

OrthicTriangle  Given 3 vertices of a triangle, construct its orthic triangle.  
Orthocenter  Given 3 vertices of a triangle, construct its altitudes and orthocenter.  
PedalTriangle  Given 3 vertices of a triangle and another point, construct the pedal triangle.  
TriangleFromSides  Given the endpoints of three segments and one vertex of a new triangle (as well as another point to define the direction of one side of the new triangle), construct a triangle whose side lengths are the same as the lengths of those segments (if possible).  
Circle Tools
Triangle Tools
Polygon Tools
Segment Tools
Misc. Tools 

Polygon Tools 

Equilateral  Given adjacent vertices, construct an equilateral triangle.  
Hexagon  Given adjacent vertices, construct a hexagon.  
Octagon  Given adjacent vertices, construct an octagon.  
PentagonRadius  Given the endpoints of a radius of the circumscribed circle, construct a pentagon.  
PentagonSide  Given adjacent vertices, construct a pentagon.  
Square  Given adjacent vertices, construct a square.  
Circle Tools
Triangle Tools
Polygon Tools
Segment Tools
Misc. Tools 

Segment Tools 

GoldenRatio  Given the endpoints of a line segment, divide the segments
into two shorter segments whose ratio is the golden ratio. (This construction came from http://www.geocities.com/robinhuiscool/Goldenratio.html) 

TrisectSegment  Given the endpoints of a line segment, trisect the segment.  
Circle Tools
Triangle Tools
Polygon Tools
Segment Tools
Misc. Tools 

Misc. Tools 

LocusVertexSubtend  Given the endpoints of a segment, and three points defining an angle, construct the locus (which is a circle) of the vertex of an angle of the given measure subtending the given segment.  
Circle Tools Triangle Tools Polygon Tools Segment Tools Misc. Tools 