First, there's Wikipedia's article on sidecars, which at the top describes some of the physics of using a sidecar, as applied to motorcycling. The same physics are in effect on bicycle, but the main difference is the lesser weight. Also from Wikipedia, under cycle rickshaw, the Filipino-style BMX sidecar.
Then we have the Burmese sidecars that are the Myanmar way to travel. Check out the size of that klaxon!!
In Singapore, sidecar trishaws are also common. And not all of them are half a century old, either, as this Travel Folio shows.
A swiss company, Smike, offers a purpose-built electric bicycle with a quick-releasing detachable sidecar.
Here's a Sidecar gallery on Flickr.
From an off-road fixed-gear junkie comes this machine.
This is the only company I know of in the United States that is trying to produce sidecars, Jeinkel-Heimer.
Not large enough for pedi-cabbing, but these old Watsonian sidecars from the 30s exhibit exemplary style. I like the very simple design, utilizing a pivot and spring suspension
Nice website: Velo-city.org. There's a decent page on sidecars, though they seem to be a bit critical about the form as a stronger element than the function. In the pedicab world, though, people notice the shape of your cab before they notice how it performs, so it can be a major plus to look goofy but cool at the same time, as long as its performance is safe and satisfactory.
The kustom page.
And this one strikes me as incongruous:
A sidecar, with checkers and "Yellow Pedicab" printed across the side, yet it appears to be selling pizza and not pedicab rides!