As you might guess, parking in China -- or at least in Shanghai, which is a high-density, land-at-a-premium city -- tends to be a little different from in much of the US.

This (left) is the most common form of parking lot. It usually (but not always) includes someone "official" wearing a crossing-guard vest to take your RMB1 and ostensibly make sure no one else takes your bike. Motorcycles sometimes park in these lots too, which fits with the generally-shared delusion here that motorcycles are really just like bicycles.
Note that most of these bikes are not locked to anything; there's just a lock that clamps around the wheel and prevents someone from riding it away. Kind of like The Club for a bicycle. I guess the assumption is that if someone has the means to cart your bike off without riding it, they don't want your stinky bike anyway. Or maybe those locks are just a lot better than I think.

There are pieces of land that the average American could identify as a parking lot. But at least in downtown and the nearby vicinity (the suburbs are a different matter), they tend to hold only a handful of cars, and are frequently accessed by driving up onto the sidewalk. I'm not kidding.
More common are the garages that I like to think of as car apartments. I know there are some of these in NY, SF, etc., but can't think of any in DC. I still think they're nifty.

For those of you who have not had the pleasure, these garages maximize space by getting rid of ramps... and drivers. You pull your car into the elevator, step outside, and watch it get whisked away to an unknown floor. I've heard some people dislike them because (as with valet parking) you have to wait to get your car back. Frankly, I think it'd be worth it to not spend time trying to find an empty slot.