The code you are using to select a color is working.  The problem is that you are changing the fill color in the draw() routine, in order to draw your color palette.  This obliterates the color you previously set in the mousePressed() routine.

Hmm.. that doesn't seem to work.

1. int fillColor;
   boolean drawing = false;
   
   
   // setup - runs one time
   void setup()
     {
     // set a stage size of 500 x 500 pixels
     size (500,500);
   
     // smooth all drawing
     smooth();
   
     // don't draw an outline around your shapes
     noStroke();
     }
   
   // draw - runs once a frame
   void draw()
     {
     // draw a color button
    
     fill (255,0,0);
     rect(0,0,100,50);
    
     fill (0,255,0);
     rect(100,0,100,50);
   
     fill (0,0,255);
     rect(200,0,100,50);
    
     // are we in draw mode?
     if (drawing == true)
       {
       ellipse(mouseX, mouseY, 30, 30);
       fill(fillColor);
       }
   
     }
   
   // mousePressed - runs every time the mouse is pressed
   void mousePressed()
     {
     // did we click the button?
     if (mouseX > 0 && mouseX < 100 && mouseY > 0 && mouseY < 50)
       {
       fillColor = fill(255,0,0);
   
       }
   
     if (mouseX > 100 && mouseX < 200 && mouseY > 0 && mouseY < 50)
       {
       fillColor = fill(0,255,0);
   
   
       }
   
     if (mouseX > 200 && mouseX < 300 && mouseY > 0 && mouseY < 50)
       {
       fillColor = color(1);
   
       }
         
   
     // otherwise we are in draw mode
     else
       {
       drawing = true;
       }
     }
   
   
   
   
   void mouseReleased()
     {
     drawing = false;
     }
   

1) Call fill(fillColor) *before* you draw the ellipse, not after.