tl;dr drag the icon of another applet or launcher that is next to the green cross to another place and the green plus should disappear
If you wanna read the long story..
Earlier today, when I booted up my ubuntu, I noticed a wierd green cross/plus icon on my AWN dock. I use AWN because I don't like the ubuntu's native launcher and the other ones I've tried (cairodock, docky) have all crashed so much that I don't ever want to think about them again.
Anyway, I noticed this green icon... and naturally I wanted to know what it was. I put the cursor over it (thinking it was an unnoticed launcher) but no text showed up. Hmm... that's weird. Let me see if I can remove it. Right click (like any sane being would)! Nothing. Double click...Nada! I could virtually do nothing to know what it was, why it was there, and couldn't remove it by any means!
At this point, I was extremely frustrated but not to the point where I wanted to pluck my eyeballs out.
It was a waste of time. The people who asked the question moved on to use other docks because that icon was so annoying.
I gave up and went back to what I was doing. Then randomly, I tried to drag another icon that was next to the green icon --- and what do ya know? It was gone. Like that! My sanity was restored.
So friends, the lesson here is: if you face a problem that seems like it has no solution, do the most random thing you could think of and hopefully you'll find the solution.