Great thread.
First thing I'd like to say is that a bike (pedal or powered) is one of those great 'preps' because it bears the hallmark of a great 'disaster preparedness' item. That being It's a good idea irregardless of wether or not the "shtf". If the fan is soiled, you have somethign you can use. If the fan is clean, you have something you can use. "Preps" that are only good if the world ends but are useless untill then are just a waste of resources. A bike you can have fun with right now.
OK, down to specifics. A pedal bike is a great thing. My son is just getting his riding legs, so I'll be getting a bicycle for next year so we can ride around together. I'm definitely going for the foam 'innertubes' that never go flat. In a disaster, a bicycle and some rope can become a cargo carrier. Ride to where you need to get something, strap it on and walk the load. Is that thief bait? Maybe. Maybe not. Kind of depends what the situation is. If it's too risky to travel then that's that, but a disaster may or may not look like that. Maybe the shtf in a small way, and you are out there trying to wipe the poop off the fan blades. Why not have a bicycle? Another point, riding a bike is as good a way to get a little exercise as anything. Back to the 'good if it does or doesn't hit the fan' thing. It's not a bad idea to get a little physical activity in now, is it?
I like the Whizzer type motorized bicycle thing that was posted. It's just cool. Again, might be a neat thing to have for picking up milk and bread during the good times. Now in a pinch, those simple little one lung engines are way easier to convert to improvised fuel than a modern computerised car, and you can go further on whatever you are 'stilling with a light weight vehicle. (for those who want to play with alternative fuels, one of those is a perfect test platform) Again, if travel isn't safe, it isn't safe; but if you need to go 20 miles and get help before a loved one expires then a motorized bicycle would be a blessing. Don Heath, how do you think the locals in your area would welcome something like that? I'll bet they'd love it.
Moving up to the motorcycle. Why not? If you want a vehicle that can go fast, or go where few 4 wheelers can, then a motorcycle is it. In a jam, it could be the difference between getting to safety or just not getting to safety. In the mean time, a nice motorcycle ride is just a wonderful thing. It's like a vacation that you don't have to go far for. Just start it up, and go.
All the options offered so far in this thread have aplication in good times or bad. Sure, you can think of a scenario where any of them may not be ideal. You can also see where they may be perfect. Since there is no knowing what tomorow brings, just get whichever one (or combination) you see as being good today. Enjoy it now. Ride a bicycle for a little fitness. Take a Kowi on the trails. Get a motorbike or moped to buzz around cheap. No bad ideas here.
An afterthought on the motor bike. The first vehicle made by Honda was an improvised motorbike. Mr Honda (can't remember his 1st name) owned a factory that made piston rings before and during WWII. His factory was leveled during the bombing toward the end of the war. When the war ended, Japan's roads weren't looking good and gasoline was a rare commodity. He bought a bunch of small motors that had been meant for running generators and designed mounts to put them on existing bicycles. He converted them to run on turpentine (which they produced in Japan, unlike petroleum) and a motorcycle dynasty was born. I don't know if there are any surviving examples of Honda's original post apocolypse vehicle (it really was post apocolpse for a while there, untill the American rebuilding effort got under way). If any are in a museum somewhere, I'd love to look at one.