How do I bring back lost Kerbals?

In Sandbox Mode, Kerbals don't die. They "mysteriously disappear".

They respawn after a short while (the original three (Jebediah, Bill, Bob) at a quicker rate than generic Kerbals), and can then be sent to their doom again. And again. And again.

If you want them back to life immediately rather than waiting, you can open your KSP game folder/saves/username/persistent.sfs with your favorite text editor, find ROSTER and change the crew members' statuses from state = 3 to state = 0. This will instantly revive your Kerbals.

I'm not sure if it matters whether the game is running or not, but I would make sure and edit the file while the game is not running.

Source on KSP forums