Have you ever experienced "a deep, severe pain that starts low on one side of the back and then shoots down the buttock and the leg with certain movements"? If so, according to http://www.emedicinehealth.com/, you might have sciatica. Any time you have deep pain, it is best to seek medical advise from your doctor. Please, use the information here as an aide and not as medical advise--which I'm not qualified to give.
With that said, if you have sciatica, the following exercises may bring you relief. Remember the cause of your pain will influence the helpfulness of these movements. Your doctor or therapist may be able to pin point the root of the problem. Dr. Jean-Jacques Abitbol, orthopaedic surgeon and founder of the California Spine Group, says that the six leading causes of sciatica are a bulging/herniated disc, lumbar spinal stenosis, spondylolisthesis, trauma, piriformis syndrome, and tumors. So, you can see why it's important to have a diagnosis made.
In the case of piriformis syndrome, the exercises below will have the most success (as always check with your doctor first):
Supine Hand to Big Toe Pose - Supta Hasta Padangusthasana
Supine Hand to Big Toe Pose, but this time cross the top leg just past your midline. Root down through the outer hip crease at the same time.
King Pigeon - Rajakapotasana while leaning forward. Be sure to align the sacrum, that is do not allow one hip to fall lower than the other.
Half Lord of the Fishes - Ardha Matsyendrasana
Cow - Gomukhasana
Asanas to be Careful with
Be sure that all forward bends come from the hip crease and the pelvic bowl tips forward.