For transparency, I would try the Alpha value (or opacity) in the assignment (see color()), which would look like this:
color(red, green, blue, alpha);
Of course, you need to make sure that the file type supports transparency.
If that does not work, I think I've heard of something involving the value 256 to be transparent, as in:
color(256);
But again, not all filetypes support that.

Yes, just use a PGraphics in Java2D mode.

Heres a real basic example doing what phi.lho said. I did have some success rendering transparent 3d objects using P3D as well.

1. PGraphics pg;
   
   void setup(){
     size(800,800);
     pg = createGraphics(400,400,JAVA2D); //create the off-screen graphics
     pg.smooth();
     pg.beginDraw();
    float diameter = 150;
    pg.noStroke();
    pg.fill(0,128);
    pg.ellipse(pg.width/2,pg.height/2,diameter,diameter);
    pg.fill(255,196);
    pg.ellipse(pg.width/2,pg.height/2,diameter*0.9,diameter*0.9);
    pg.endDraw();
    pg.save("transparent.png");
   }
   

- Kyle Phillips

Ah, looks like my advice is partially obsolete. There was a time where P2D didn't allow transparent background, but I see now it works as well as JAVA2D (at least in 0193, I don't know when the improvement was done).

Wow thanks for all the input so quick!

PGraphics does work but I have a very complicated sketch which brings in and parses xml data and then writes it to the screen so Id have to do a lot of restructuring. 

But with your help and motivation to figure it out I was able to find that you can save as a PDF http://www.processing.org/reference/libraries/pdf/index.html import file into Illustrator, and choose png under save for web and devices and it holds the transparency that PDFs can make when there is a white background.  This works better for my needs because I want to print the sketches individually on a large scale and the PDF vector works better for that.

Glad we figured out a few options and this is now here as a reference.

Cheers.