Hard drives aren't permanent. If you believe that your photos are entirely safe on your computer's hard drive, you may be in for an awful surprise.
No matter how space age-y your computer might feel, it's important to understand that it's controlled entirely by physics. Parts degrade, pieces fall off and must-have data could be lost.
The problem with storing images on your computer is the number of moving parts that can break. Over time, the failure rate of a hard drive is 100%, which means that the drive could lose all of the data stored inside.
The safest place for your photos could actually be to keep a printed copy or two lying around your house.