You're right, scratchypants, thanks. I checked and Xenforo has no default favicons in the software, so browsers or Google create one.
I just played with creating a couple with an online favicon generator, but they didn't look good. It has to be a 32x32 png image, which then has to be hosted somewhere on the web so there is a linkable path to it that I can put in the root folder. Maybe I should let members try to create a favicon for the site.