In the future I'll be doing this on a case by case, consulting basis. This one, though, will be free 
Well If it weren't for that fact that as long as I've been using this website (about 3 years) I've never seen anyone tell this story, I would feel redundant repeating it. The short version would be to say it was just like getting nearly missed by a boat, the main difference in the scenario only coming at the last few seconds. When you realize the boat isn't aware of you, as Dan said, you start to calculate how to navigate the situation. So anyways here is what happened to me.
I was yak diving off Hollywood beach, on the outside of the second reef. For reference thats somewhere around 1/2 mile out (someone correct me if I'm wrong). The water was flat and it was still early and the wind was low. A few things worth noting are that I was diving alone and using a good friend's kayak. Because of these two factors I was sticking very close to the anchored kayak. The reasoning being that when I shoot a fish alone I like to be close to the kayak to toss it in quickly and more importantly being that when using other people's things I get paranoid about them being lost/ damaged etc. If my little kayak's anchor uproots and ends up washed ashore miles away I can deal with that. Losing something entrusted in you is different. Anyone diving anywhere in South Florida from the third reef in to shore is plenty accustomed to nuisance boat traffic. Also, as Dan pointed out, boaters are a dangerous mix of negligent and curious regarding divers. As soon as I hear a boat I always look where it is, and generally dismiss it and continue diving. On this day I could see the boat (a forty something foot Searay about 1000+ yards away) coming what looked like straight at me. This is not unusual as many boats from that distance appear to be honing in on you. So I probably made two more dives ignoring the growing engine sound before I decided to look again. The boat was then within 100 yards and from that distance it was apparent that without turning he was going to cross directly or within a few feet of me. I was still within 15 feet of the kayak. So I bobbed and watched the boat get closer and closer. Considering its quick pace I decided to dive down with what I thought was about 20 seconds until its arrival. So dive I did, and I looked up once I had reached about 30 feet deep (about 5-8 feet up from the bottom). The second I looked up is the second the boat passed directly over me. I saw the kayak shoot out to the side as the boat grazed parallel to it and after that I saw the paddle (which was tied to the yak and resting in the yak) come down in around 6 pieces. Also the anchor line was cut about 10 feet from the point in which it was clipped by a caribiner to the kayak. Despite the boat having passed I felt the need for some reason to stay down and just watch upward for about a 45 seconds- a minute. When I surfaced I didn't account for all the white wash and waves and it was a bit disorienting. Also the kayak was drifting away pretty quickly. I swam to the kayak and grabbed the side and just laid my head on it for a second and reoriented myself. Nothing in the kayak was dislodged (hatches, gear under the bungees, etc.) The guy was a captain delivering the boat and he was obviously a bit freaked out. he prob initially thought he killed someone when he looked back and saw an empty kayak. He backed up, I climbed onto the dive platform and tied the severed anchorline to a cleat and just told him to take me to shore. I didn't want to talk about it or anything, I felt like I just had some mediocre sex and just wanted done with it. (there may be a better analogy out there) He got me reasonably close to where I had put in on the beach and about 150 yards out from shore. I told him as of now I am out a paddle, anchor, anchorline, and I dont know if the kayaks damaged. He gave me his business card and I was satisfied enough and swam the yak back into shore. So in the end the yak wasn't damaged and he paid for everything lost. The thing that angers me about the whole ordeal is that people drive boats so close to shore.