Unity Shape Key Tutorial
Here's how you integrate shape keys into Unity in the new version (4.3+).
This is a super-cool feature, and here's a step-by-step instruction as to how to get it working.
If you're saving your blender file into your assets directory just fine, but the morphs aren't showing up, remember that this does NOT play well with morphs such as mirror or solidify. Apply those morphs before creating the shape keys. That's a Blender issue.