Capturing motion in photo shots

Taking photos with moving subjects can be tricky because the wrong shutter speed will result in the subject not being in focus. Since I started taking photos I have experience many frustrating moments when I view my photos on the computer. They always don't turn out the way I want them to simply because the subject matter is out of focus :( I came across advice given while going through various threads in a forum and the recommendation or rule of thumb for capturing motion in photos are : 1/30 for jogging speed 1/8 for walking speed