It really is constantly amazing to me how few books and classes address the issue of urban people who don't have cars. On the other end, you're legally required in most states to have the kid in a car seat to bring him home, but no mention is made of what you need to do if, say, you want to take the subway home or live close enough to walk. So weird.
That said, I received the following advice in childbirth class (after I specifically asked): Do NOT tell the cab company that your wife is in labor. They can't refuse to give you a ride, but they may take a really long time. It will deter them from helping you because of the potential for a)her water breaking or other bodily fluids leaking in the car b)a serious emergency/cop calling/baby delivery hassle. Also sometimes women in labor puke. The whole thing is a really big hassle basically, and all things being equal, most cab drivers would prefer to just avoid it.
We think we're going to be able to get a ride, but in the event that we have to take a cab, my husband and I have the following plan: a)try to avoid them knowing I'm in labor until we're physically in the car b)bring a garbage bag and blanket to lay on the seat c)bring a wad of cash, like 100 bucks, in case things just go terribly terribly wrong and messy so that we can throw a big tip at the driver to get the cab cleaned and then scram.