Images don't show up in Blogger posts

I struggled for a while trying to get images to show up using Blogger.com. After I discovered the reason, I thought it would be nice to post it in case anyone else had the same problem.

I host my sites independently and use Blogger.com to add content, so this advice applies to a setup similar to my own.

Your image file must not have spaces in the name. That was my problem. Use underscores to give the effect of spaces if that's important to you.

Bad: Picture of me.jpg (won't work)
Good: Picture_of_me.jpg (will work)