UPDATE MARCH 24, 2016
After some further thinking, To maintain consistency I decided to go with Winkle-bot for all three images:
Captcha, 404, and Error Winkle-bots
These will be live with the next production build.
UPDATE MARCH 23, 2016
Based on the feedback below, here are three ideas for the error, 404, and captcha images:
Error: While I can't change the headline on the page as suggested in this answer, I can place this common Magento error message within the image.
404: So the thought here is Magento is an e-commerce platform. This means people buy things. Things are shipped in boxes. Boxes can be stacked. Box stacks could be made to look like numbers with some conveniently placed forklifts.
Captcha: This is a computer sporting Phil Winkle's hair.
For those who don't know me: Hello! My name is Joshua and I'm a Senior Product Designer at Stack Overflow. I've been working on your community site theme. (I hope you've been enjoying it.)
There is one more thing to finish and I could use some help. On all our Page Not Found (404), Error, and Captcha pages, we customize images for each community. Some examples are:
Academia's error page helps communicate that something is currently "off" be tilting the tower in the header.
Cryptography's 404 page uses a puzzled John Nash (played by Russell Crowe) from "A Beautiful Mind" to show that we're all looking for something.
Movies & TV's captcha page uses HAL 9000 (from "2001: Space Odyssey") to help verify people interacting on the site are humans and not robots.
As you can see in the three examples above, these pages are a way to further express the site's topic—even when things go awry.
Typically these are designed when we launch the website, but I struggled to come up with interesting ideas prior to the site launch. And as it isn't a required element, we delayed it hoping the following weeks we would do them. Despite the best intentions though, we still have not done this and the main reason is I'm still stumped on ideas.
So can you help? What ideas for error, page not found, and captcha pages do you have? Help me create some unique and interesting pages for Magento.