Scott hasn't responded back yet so I'll chime in here. Yes, if someone is say having a heart attack you would say "call 911."

Now just to be clear and throw a monkey wrench in this.... Last month a bicyclist was struck by a car right as I was walking out of a building, she had a helmet on and was not hurt too badly and didn't want to go to the hospital or anything. But, I still said to her "I'm going to call for an ambulance. You really should let the EMTs take a look at you."

If I'm at home and some one is ill and we aren't certain if we should go to the emergency room (ER) or wait and see the doctor in the morning I would say "Do you want me to call the doctor?"

Now, back to question about a taxi or cab...in person, say on the street, you "hail" a taxi or cab. Via the phone or Internet, you "call for" a taxi or cab. Or someone is asking you if you need a cab they might say "Can I get you a cab" or "You need a tax sir?"