Do you want accuracy or precision?
Precision: 8 bits over -2 to +2 g, which is about 16 mg for the LSB, which works out to give you about 1 degree resolution.
Accuracy: The zero-offset is +/-40 mg, or just under 3 degrees.

Take-home answer: You can tell how well you are oriented to vertical to within about 3 degrees. You can measure rotation differences of about 1 degree.

Specs taken from datasheet at http://www.st.com/stonline/products/...6/lis302dl.htm