I had back surgery in 2004 due to a herniated disk in my lower back. The disk was pressing on the nerve that controls my left calf. I had no pain, or other usual back symptoms, but I lost all strength in the left calf and could not run correctly. When I talked to my surgeon, he said he would not necessarily advise a non-athlete to have the surgery, but if I wanted to continue running, I had no choice. He was particularly concerned as weakness and numbness are signs that the nerves are being damaged, whereas pain is a sign the nerves are being irritated.
I had a microendoscopic discectomy (MED) to remove the excess disk in March. The surgery was successful, as way my recovery. I have had no side effects or problems at all. However, I did follow my surgeon's directions for the recovery very closely. I did not sit for two weeks after surgery - I had to lie down or stand up. For the next four weeks, I did no running, but I walked a lot. I was told that walking was good for my back and to walk as much as I liked. (My wife commented that the Surgeon may not have meant 30 miles a day!) When I started back running, I was very cautious, not just for the back, but for the rest of the body that had atrophied. I ran just 2-4 miles every other day for a few weeks, building it up slowly. It is important after a serious injury to reevaluate your fitness level and start your training based on that fitness level. Trying to train as if you are as fit as you were before the injury will just create another injury.
Since my back surgery, I have been very aware of my back. I work at a computer all day, and have a desk that allows me to stand. I am very careful about lifting anything. When I run, I am particularly aware of steep down hills - if the foot lands with the leg straight, this will put immense stress on the back. Of recent I have established a routine for strengthening my core, but I have not always been so diligent.
Below are some images I found useful that show what part of the body has sensation from nerves originating in particular parts of the spine.