You're going to need to create a boolean that defines when the mouse is pressed and two ints (x and y) that define where the mouse was pressed; when mousePressed() is called, set that boolean to be true and the x and y to be the mouse location. In draw(), if the boolean is true, display the rectangle with the x, y, and current mouse location. When mouseReleased() is called, set the boolean to be false.

That probably sounds complicated, but it really isn't...
You can look at the Mouse Functions Example for how to use the mouse functions...
Take a look around the examples page for more...

1. int pointX = mouseX;
3. int pointY = mouseY;
4. boolean mousepressed = false;
5. 
   
6. void setup(){
7.   size(400,400);
8. }
9. 
   
10. void draw(){
11.   background(255);
12.   noFill();
13.   rectMode(CORNERS);
14. }
15. 
    
16. void mousePressed(){
17.   if (mousepressed = true);
18.   int pointX = mouseX;
19.   int pointY = mouseY;
20. }
21. 
    
22. void mouseDragged(){
23.   rect(pointX,pointY,mouseX,mouseY);
24. }
25. 
    
26. void mouseReleased(){
27.   mousepressed = false;
28. }

Thank you for any help.

You were pretty close. Actually there already is a built-in boolean in Processing called mousePressed.

Adapted Code

1. int pointX, pointY;
2.  
3. void setup() {
4.   size(400, 400);
5.   rectMode(CORNERS);
6. }
7.  
8. void draw() {
9.   background(255);
10.   // only display when the mouse is pressed
11.   if (mousePressed) {
12.     rect(pointX, pointY, mouseX, mouseY);
13.   }
14. }
15.  
16. // when the mouse is pressed set the starting coordinates
17. void mousePressed() {
18.   pointX = mouseX;
19.   pointY = mouseY;
20. }

Advice:

That sounds like you need to store the mouse presses in a permanent place; for example, using an ArrayList.
Every time that you receive a mouse press, you add an element to the ArrayList; then, every time that you receive a mouseReleased() call, you add an element to a different array.

Example:

1. //Create an ArrayList for the presses and the releases
2. ArrayList<PVector> pressLocations;
3. ArrayList<PVector> releaseLocations;
4. 
   
5. void setup() {
6.   size(400, 400);
7.  
8.   //Initialize the ArrayLists
9.   pressLocations = new ArrayList<PVector>();
10.   releaseLocations = new ArrayList<PVector>();
11.  
12.   //Set the rectangle drawing mode
13.   rectMode(CORNERS);
14. }
15. 
    
16. void draw() {
17.   //Referesh the background
18.   background(255);
19.  
20.   //Cycle through the presses
21.   for(int i = 0; i < pressLocations.size(); i ++) {
22.     //If the mouse is still being pressed (or, rather, it hasn't been released yet)
23.     if(i >= releaseLocations.size()) {
24.       //Draw a rectangle from the press location to the current mouse location
25.       rect(pressLocations.get(i).x, pressLocations.get(i).y, mouseX, mouseY);
26.     } else {
27.       //Draw a rectangle from the press location to the release location
28.       rect(pressLocations.get(i).x, pressLocations.get(i).y, releaseLocations.get(i).x, releaseLocations.get(i).y);
29.     }
30.   }
31. }
32. 
    
33. void mousePressed() {
34.   //Add a press
35.   pressLocations.add(new PVector(mouseX, mouseY));
36. }
37. 
    
38. void mouseReleased() {
39.   //Add a release
40.   releaseLocations.add(new PVector(mouseX, mouseY));
41. }

Implementation:

Sorry to leave the implementation to you, but I'm rather crunched for time right now...

This new requirement has two consequences:

1. The ellipse needs to be displayed even when the mouse is not pressed.
2. You need end coordinates that are independent of the mouse.
   

Thanks guys. Reading the code from both of you has helped my understanding quite a bit. It seems to make sense when reading it but then writing it is a different story haha.