Set up some appropriate boolean variables and test against these to determine what is drawn when, and call background() every frame...

Cheers Blindfish,

blindfish's method is "the normal way" of Processing sketches.
If you really need/prefer to have a static sketch, you can just draw a rectangle over the area to clear...

My problem is that I am developing an annotation application that allows users to annotate processing sketches.  They have a range of simple paint tools  - from drawing to labeling.  However, if I call background, all the previous annotations - by that user - disappear.  However, If I do not call background(255); then the application turns into a series of black, messy lines as the user draws on the screen.  

I am developing an annotation application that allows users to annotate processing sketches.

Intriguing...

Anyway - instead of drawing the annotations directly to the screen, how about drawing them to a separate buffer image which you then draw over the screen each frame; then background() calls in draw won't affect them.

This is roughly what I had in mind:

1. PGraphics annotationBuffer;
2. boolean annotationsDisplayed;
3. 
   
4. void setup() {
5.       size(###,###);
6.       annotationBuffer = createGraphics(width,height);
7. }
8. 
   
9. void draw() {
10.       background(0);
    
11.       // render your processing sketch
12. 
    
13.       if(annotationsDisplayed) {
14.             image(annotationBuffer,0,0);
15.       }
16. }
17. 
    
18. // not sure how you're handling this, but you should get the idea
    
19. void annotate() {
20.       annotationBuffer.beginDraw();
21.             //draw annotations direct to the buffer
22.             //...
23.       annotationBuffer.endDraw();
24. }

Annotations are kept on a separate buffer which is also drawn to the main display (you even have the option to switch them off if required by switching the boolean).  Then to export your final image you simply take a grab of the main display, which includes the annotations.