Which sets can be built in the bag (all the parts are in one bag)?
The ones I know of:

8072 - Sea Jet
8400 - Space Speeder
8398 - BBQ Stand
5611 - Public Works
5762 - Mini Plane
7241 - Fire Car
8130 - Terrain Crusher
5618 - Troll Warrior
to be continued...

In addition, some LEGO Creator sets, with only partly transparent bags are possible to build in bag, like this video shows - but it gets a lot harder.
Rather then listing all of the sets, I'd go by the general rule that sets that are 9.5cm x 9.5cm x 4.5cm or smaller are in one bag (or just in the box). The Court Jester (7953) for example, is one exception in that the Jester hat is packaged separately.