How to turn this:

into this:

Step 1) Install GIMP (Gnu Image Manipulation Program - free and open source): http://www.gimp.org/downloads/

Step 2) Install the MathMap plugin (also free): http://www.complang.tuwien.ac.at/schani/mathmap/

Step 3) Find an image to turn into a globe - the width needs to be twice the height.

Step 4) Load the image in GIMP

Step 5) Select Filters->Generic->Mathmap->Mathmap

Step 6) Cut and paste the script at the bottom of the page (or download it here )

Step 7) Click the Preview button to see a preview of the transformation

Step 8) Change to the "User Values" tab where you can change the number of petals and shift the image left / right

Step 9) When you're satisfied with the preview, click OK to run the transformation

Step 10) Print / Cut / Paste - or - Tape into (or onto) a sphere.

Another example - the 2010 Maker Faire Map click here for a larger version:

Here's the mathmap script:

#-----------------------------------------
# This slices an image with a 2:1 aspect
# ratio into a a form that can be cut 
# and glued into a globe
#-----------------------------------------

filter sinusoidal(int divs: 3-30 (8),
		  float pan: -180-180(0),
		  image in)    


#divs - Number of divisions to create.
#pan -  Panning left / right to align petals 
    py = -2;
    counter = 0;
    
    while (counter <= divs) do
      px = if (x>1-(2*counter/divs)-1/divs && x<=1-(2*counter/divs)+1/divs) 
           then (x-(1-(2*counter/divs)))/cos(y*pi)+1-(2*counter/divs)+W*pan/360
           end;
      if (x>1-(2*counter/divs)-1/divs && x<=1-(2*counter/divs)+1/divs) then
        if (px<=1-(2*counter/divs)+1/divs+W*pan/360 
            && px>=1-(2*counter/divs)-1/divs+W*pan/360)
           then py=y
           else py=py
           end;
      end;
      counter = counter + 1;
    end;

    #allow the x axis to loop around
    if px<-1 then px=px+2 end; 
    if px>1 then px=px-2 end;

    if py<-1 then
	grayColor(1) #or .95 for a light gray background
    else 
	in(xy:[px,py])
    end
end