Not so much a "game" as an interesting exercise. Google image your avatar name and post the first (or most interesting) image that pops up.
beardedinlair
(http://www.oocities.org/robotatomic/images/karloff.gif)
This was actually the third image on the page:
http://zipolo.deviantart.com/art/Uncle-Yuan-83970365
Clearly someone made it for me, and according to the description it was for a secret santa. I do recognize the picture, but a I am very ashamed to admit I no longer have the slightest idea who made it for me.
I searched "The Holy Pilgrim avatar", and this is what I got as the first result:
Spoiler
(http://www.twcenter.net/forums/customavatars/avatar50462_18.gif)
That is actually my current avatar over at the Total War Center :P
Woah now, some mouse is cramping my style!
Typing my avatar's name, Reep the Barbarian was slightly more interesting:
Spoiler
(http://faces.cohtitan.com/render/image/large/0/80261.jpg)
It's... me! That's my face! From, like 5 years ago!
I got this
(http://img.photobucket.com/albums/v58/moonshadow386/The%20Lady%20of%20Shalott_zpsewiice0s.jpg) (http://smg.photobucket.com/user/moonshadow386/media/The%20Lady%20of%20Shalott_zpsewiice0s.jpg.html)
I just love that Painting