Good for:
Hustling backstage during a tight show with short changes
Improving your overall balance in heels (Running in heels will turn you into a pro at walking in in heels, trust me.)
Developing toned calves
Catching a bus or hailing a taxi
Rushing through busy city streets while also not getting your stiletto caught in a storm drain or grate.
Fleeing your enemies

VERY IMPORTANT:
Do not do this unless you have strong ankles, core strength, and intermediate comfort in heels (This is a oneway ticket to Sprainedankleville if you're trying to run without first learning how to walk with basic form and proper posture.)
PLEASE wear the right size shoe. Too big a shoe can cause your footwear to slip off, which can be dangerous. If possible, select a shoe with a strap so your foot is firmly attached.
Practice with a shoe you don't care too much about. It's going to add some wear and tear, especially along the bottoms.
Don't run for too long... running in heels keeps your achilles "shortened" due to the heel being kept up. When you're done, overflex both feet with some achilles stretches to reextend and restore them again.