An avatar image is certainly not required. But it can be a fun way to create a visual identity online. I tend to use the same image most of the time, but not on all the forums I visit, as my activity in different places suggests different faces.

But within a forum, I tend to switch rarely, and if I do, use a new image related to the old image in some way, to maintain continuity. But that's just me.
I know someone on another forum who regularly changes avatar, signature, AND user name.

That's too confusing for me. I have a hard enough time remembering who I am from day to day.