When doing a Google search for "world's largest granny square", I didn't find any sort of noteworthy record. The closest I came was a blogger who had made a bedspread-sized granny square. I'm certainly going to try to make a noteworthy granny square out of this stuff:
This is what I had last time I took a picture of it, but it has since increased by several rounds:
Hopefully it will be large enough for a blanket, or at least a lapghan or a baby blanket. I'm not sure what I'll do with it afterwards... my boyfriend doesn't like the colour, so he wouldn't want it lying around the living room. Maybe I'll give it to charity or something.
One can find a decent granny square tutorial here, and probably on a gazillion other websites. It's popularity peaked in the '70s, when people were making ugly granny square ponchos, vests, and skirt and collar set. Interest in the granny square has since been revived, but fortunately, there are much prettier designs, such as those made by Robyn Chachula, where most of her designs are motif-based (that is, sewing a bunch of squares or other shapes together).