Assuming you're wanting to join two polygons that both share a common line i.e. two subsequent vertices of exactly the same points and not worry about intersecting polygons it would not be that hard to do.
A bit or pseudo-code on my thoughts...

# assuming polygon is 1-2-3-(4=1 implied) for a square
#Get both shapes going in the same direction
# to make things simpler later
Order array of shape 1 so that its a clockwise closed shape
Order array of shape 2 so that its a clockwise closed shape

foreach line in shape 1 {
    foreach line in shape 2 {
        are line1 and line two the same {
             store which line this is.
        }
    }
}
splice into array of shape1 at point of common line all of shape 2 rem
+oving the common line.
[download]

Regards Paul