Everybody Draw Mohammad Day was a thing that occurred on May 20, 2010. There's been some activity in subsequent years on May 20, but I'm not really sure how active it is anymore. Personally I consider it a success if it's not so big a deal anymore when people draw Mohammad.
In the past I've said some things about Draw Mohammad Day that were not altogether coherent. In any case, here is my retrospective opinion.
I support people who draw Mohammad. I think Draw Mohammad Day is a good way to stand in solidarity with people who have been threatened with violence and death for drawing cartoons. They can't give us all death threats!
It's also, frankly, silly that people get offended by depictions of Mohammad. As I understand it, the original point of the prohibition is to prevent people from idolizing depictions of Mohammad rather than God. I don't think there is any danger of people idolizing the drawings from Draw Mohammad Day. So this is a case of religion enshrining arbitrary rules while ignoring their original rationale.
However, I have reservations about the effectiveness of Draw Mohammad Day as a political tool. If you wanted to explain to a child why free speech is important, Draw Mohammad Day isn't exactly the kind of example you'd come up with.
"Freedom of speech is important, because it allows us to draw Mohammad, the prophet of the Islamic religion, even if it offends some Muslims."
"Why should we be allowed to do that?"
"Lots of people draw Mohammad on Draw Mohammad Day. They do it to support free speech!"
"I don't get it. Freedom of speech is important because it allows us to draw Mohammad in order to support free speech?"
In other words, I worry that the value of Draw Mohammad Day is too self-referential. Freedom of speech is important because it allows us to support free speech?
Anyway, here is my drawing of Mohammad.