1. Fix it
Eyeshadow can be fused back together with just rubbing alcohol, a spoon, and a little time. I tried it- worked perfectly. Find the detailed step-by-step tutorial on Angela Hix.
2. Eye gloss
If you don't have time to fix your broken eyeshadow, but still want to use it on your eyes, eye gloss is the way to go. Just mix baby oil and crushed eyeshadow, apply with a brush and you're done. Find the how-to on Lulu's.
3. Nail polish
Create your own nail polish in just a few seconds with clear nail polish, crushed eyeshadow, a toothpick and a piece of paper. Super easy, super quick. Find the DIY on Delighted Momma.
If you've been lucky in your misfortune and broke an eyeshadow of a color that would look nice as an eyeliner, you only need some baby oil to give it a new life! See the tutorial on WikiHow.
5. Lip gloss
Make your own tinted lip gloss in two minutes using only vaseline and crushed eyeshadow. Couldn't be easier! Find the how-to on Wonder Forest. Edit: it's been brought to my attention in the comments that some eyeshadows aren't safe for the lips. Read the labels of the products to be used, or here is a helpful link on that subject.
I hope you won't break all your eyeshadows like I did, but if that inopportunely happens to you, please consider the alternatives before tossing them :)