To answer the DIY bit about shower pans that won't fit --
They sell these kits that are basically styrofoam drain pans, that you can cut to the size you want, put down a waterproof membrane, and tile over. Search for 'styrofoam shower pan kit'.
As for how common they are, I can only remember seeing one modern (within the last 60 years?) home with wet rooms in the US, and it was more the scale that gregmac linked to, (and it happened to be my dad's house that he had built).
In his case, he had them built specifically for accessibility; they were on the first floor, where he was expecting that he might have my step-mother's mother move in. There was a slight dip as you entered (not enough to adversely affect a wheelchair, but enough to keep water from coming out), and there were hand-rails and a built-in-seat in the shower area.
However, I've been in some tiny wet rooms in Europe. The smallest (less than 5'x3'?) was in a hotel in Venice, as a retrofit -- as you entered the bathroom, there was a tiny sink to the left, and a small toilet to the right (a tankless model, or the tank was in the wall, I'm not sure how they do it in Italy); the door opened out, and there was barely space to stand in between the two. There was a rubber drainage grid on the floor, as the whole room itself was the shower. (the toilet paper roll was mounted higher up, out of the shower spray, and had a self-closing protective plastic cover). You might get some points for creativity, but I'd likely just advertise it as a half bath, and see if people notice that there's a set of controls on the wall and a shower head in the ceiling.
I've also seen some creative sink mounting, where if you have a tank on the toilet, the sink mounted just above it (but didn't come out so far that it came out past the front of the toilet tank).
Other things to consider are the doors -- I don't know why American homes always seem to have bathroom doors swing in, but if you can swing out, it'll feel much more spacious; if you have reasons you can't do that, try for a pocket door.
And the only other places I've seen wet rooms (other than older homes, with claw-foot tubs), are more industrial/commercial -- like one of the bars I used to go to. It was subtle -- there was a high ceiling with a shower head mounted almost touching it, and a sign next to it that said 'Budweiser, Rinse, Repeat'. People who had been regulars for years hadn't even noticed it. Hospitals, as Joan mentioned, they're pretty common, or hotels with a 'handicap accessible' room. Locker rooms in gyms or schools are another place.
And I agree with gregmac -- don't go cheap on it, or people might compare it to gas station bathrooms.