I suspect some sort of spy-ware or mal-ware. But it seems to be a strange symptom. The worst trouble is that I can't be sure where my cursor is when editing because the block takes up several letters at a time.
P.S. The square block cursor shows up in most text entering places (i.e. address bar, google box, notepad) but not in MS Word. In Word the cursor is a normal black line. Hmmms...