try....

note pls how x is used as a upper bound for the for-loop and that we delete the screen
with background() each time in draw()

consider cursor left  for x=x-2;

(not tested)

1. 
   
2. int grey = 180;
3. int x = 0;
4. 
   
5. ArrayList pointList = new ArrayList();
6. 
   
7. 
   
8. void setup(){
9.   size(400,400);
10.   background(255);
11.   stroke(grey,grey,grey);
12.   
13.   importTextFile();   
14. }
15. 
    
16. void draw(){
17.   
18.   background(255);
19.   for (int i = 0 ; i < x ; i++) {
    
20.     PVector v1 = (PVector) pointList.get ( i );
21.     PVector v2 = (PVector) pointList.get ( i+1 );
22.    
23.     line(v1.x,v1.y,v2.x,v2.y);
24.     
25. } // for
    
26.    
27. } // func
    
28. 
    
29. void keyReleased () {
    
30.     if(keyCode == RIGHT){
31.       x = x + 2;
32.     }
33. }
34. 
    
35. void importTextFile(){   
36.   String[] strLines = loadStrings("points.txt");
37.   for(int i = 0; i < strLines.length; ++i){
38.     String[] arrTokens = split(strLines[i], ',');       
39.     float xx = float(arrTokens[0]);                     
40.     float yy = float(arrTokens[1]);                     
41.                         
42.     pointList.add(new PVector(xx,yy));
43.   } 
44. }

Dunno if it's right. But here comes my attempt:  

final static color GREY = 180, BG = -1;

final static List<PVector> pointList = new ArrayList();

void setup() {
  size(400, 400);
  noLoop();
  background(BG);
  stroke(GREY);

  importTextFile();
}

void draw() {
  int idx = frameCount++ % pointList.size();
  print(idx + "\t");

  PVector v1 = pointList.get(idx-1);
  PVector v2 = pointList.get(idx);

  line(v1.x, v1.y, v2.x, v2.y);
}

void keyPressed() {
  if (key == ' ') {
    background(BG);
    redraw();
  }

  else if (keyCode == RIGHT)   redraw();
}

void importTextFile() {
  String[] strLines = loadStrings("points.txt");

  for (int i = 0; i != strLines.length; ++i) {
    float[] arrTokens = float( split(strLines[i], ',') );
    pointList.add( new PVector(arrTokens[0], arrTokens[1]) );
  }
}

From your description it is not clear what your goal is. Do you want to draw one more line each time until all lines are drawn or do you want to cycle through the lines one by one. If you want the former, check Chrisir's code above (but beware of out-of-bounds error!). If you want the latter, check the code below.

Adapted Code

1. ArrayList <PVector> pointList = new ArrayList <PVector> ();
2. int currentLine;
3.  
4. void setup() {
5.   size(400, 400);
6.   for (int i=0; i<10; i++) {
7.     pointList.add(new PVector(random(width),random(height)));
8.   }
9.   stroke(180);
10.   smooth();
11. }
12.  
13. void draw() {
14.   background(255);
15.   PVector v1 = pointList.get(currentLine%pointList.size());
16.   PVector v2 = pointList.get((currentLine+1)%pointList.size());
17.   line(v1.x,v1.y,v2.x,v2.y);
18. }
19.  
20. void keyPressed() {
21.   currentLine++;
22. }

Now's a version using a regular Array in place of an ArrayList:   

final static color GREY = 180, BG = -1;
PVector[] pointArray;

void setup() {
  size(400, 400);
  noLoop();
  background(BG);
  stroke(GREY);

  importTextFile();
}

void draw() {
  int idx = frameCount++ % pointArray.length;
  print(idx + "\t");

  PVector v1 = pointArray[idx-1];
  PVector v2 = pointArray[idx];

  line(v1.x, v1.y, v2.x, v2.y);
}

void keyPressed() {
  if (key == ' ') {
    background(BG);
    redraw();
  }

  else if (keyCode == RIGHT)   redraw();
}

void importTextFile() {
  String[] strLines = loadStrings("points.txt");
  pointArray = new PVector[strLines.length];

  for (int i = 0; i != strLines.length;) {
    float[] arrTokens = float( split(strLines[i], ',') );
    pointArray[i++] = new PVector(arrTokens[0], arrTokens[1]);
  }
}

Thanks for all the responses.

Having said all that, a solution involving noLoop() may not work for me.

You could also use lerp() with an interpolation variable.

Adapted Code

1. ArrayList <PVector> pointList = new ArrayList <PVector> ();
2. int currentLine;
3. float interpolation;
4. float interpolationSpeed = 0.01;
5.  
6. void setup() {
7.   size(400, 400);
8.   strokeWeight(2);
9.   stroke(180);
10.   smooth();
11.   importTextFile();
12. }
13.  
14. void draw() {
15.   background(255);
16.   PVector v1 = pointList.get(currentLine%pointList.size());
17.   PVector v2 = pointList.get((currentLine+1)%pointList.size());
18.   if (interpolation<1) {
19.     float lerpX = lerp(v1.x, v2.x, interpolation);
20.     float lerpY = lerp(v1.y, v2.y, interpolation);
21.     line(v1.x,v1.y,lerpX,lerpY);
22.     interpolation += interpolationSpeed;
23.   } else {
24.     line(v1.x,v1.y,v2.x,v2.y);
25.   }
26. }
27.  
28. void keyPressed() {
29.   currentLine++;
30.   interpolation = 0;
31. }
32.  
33. void importTextFile() {  
34.   String[] strLines = loadStrings("points.txt");
35.   for(int i=0; i<strLines.length; i++){
36.     float[] coords = float(split(strLines[i], ','));
37.     pointList.add(new PVector(coords[0], coords[1]));
38.   }
39. }

noLoop() & redraw() only works for pure event/react driven programs!
That is, the program awaits for a user to press/click something.
While awaiting, it does nothing! It's a real saver for CPUs/GPUs/APUs!  

But once you need a program to do something else while awaiting for an user's input,
you have to abandon this "hack" 

Moreover, you can't use frameCount as an index substitute and must provide your own variable for it!

... your first code returns "Cannot find a class or type named List".

I still use Processing's current stable v1.5.1.  
To make it work w/ newest beta versions, you need to -> import java.util.*;

Or an even easier solution, replace List for ArrayList!  

amnon.owed, that's fantastic.

GoToLoop, thanks again, it's been very instructive looking through both examples, and your comments.