Our first was a bit of a production. We received a diagnosis of intrauterine growth restriction early on in my wife's pregnancy, so we had to do weekly ultrasounds quite early. At one of those, the doctor looked pretty worried. My wife was pretty oblivious, but I started looking at the monitors, and noticed a fall off in the growth chart. When the doc left the room, I told my wife that she was going to be induced that day. She was skeptical. Three minutes later, the doc comes back. Needs us to immediately head to the hospital. Recommends an ambulance, but we decline. He says fine, but there's no time to even stop by our house (12 minutes away, if you hit every light) to get the labor bag.
So, that was scary. But, don't you worry: even though there was no time to get the overnight bag, there was plenty of time to make us fill out paperwork before checking in my wife. Maybe we should have taken the ambulance after all.
It turned out to not be a giant deal. Our daughter wasn't born until the next day, after around 16 hours of labor. She was around 4.5 pounds, so she was pretty wee.
Our son, on the other hand, was a result of natural labor. I had just sat down at a settlement conference and I got the call. My wife's water broke at JC Penny. I rushed home, picked her up, and after about 7 hours our son was born. We had a brief scare with preclampsia (?) with buzzers going off, but that was short lived.