Toddler falling down the stairs
I had my daughter fall off our first stair when she was first learning to walk, and later she fell down about 10 of our 12 stairs when she was a bit older.
When she fell off the first stair, she fell flat on her face and bloodied her nose--definitely hit her head.
When she fell down the stairs, she most likely slid on her belly--she had snuck away, so I didn't see it actually happen, but rather heard the booms and cries (my husband was supposed to be watching her, but that's a whole different post).
In both cases, we called the doctor, and in neither case were we instructed to go to the hospital or come in for a visit. I think the fall would have to be very bad or cause serious injury, like a concussion or broken limb, to require a hospital visit. Most of the time, although it's very scary and most likely painful, tumbles down the stairs just require comforting.