Careful inspection of page 35 (figure 58) of the ADXL345 datasheet shows that under gravitational loading only, the chip uses a left-handed coordinate system. My own experiments with this chip confirm this.
I typically only use the chip to indicate the gravity vector. So when using this chip, I simply negate the values to get a right handed coordinate system. But this doesn't seem right. I assume there is a logical and mathematical explanation for the left-handed coordinate system but i can't figure out what it might be.