Charlie Higson's Young James Bond series has me thinking: Which of your favorite characters would you like to glimpse in their younger days? This can take the form of a flashback or entire novels.
I notice Rick Riordan has a children's series based on the adventures of Perseus. Also authors like Lee Child and Robert Crais have occasionally flashed back to fill in their protags' backstories.
Filling in can also backfire. I was excited about the Star Wars prequels, for example, but they turned out to be largely unnecessary and poorly dramatized backstory.