Bottom bracket with built-in internal hub - does this exist?
The Schlumpf drives have been around for several years and incorporate a two-speed planetary gear drive attached to the bottom bracket. With the heel of your shoe, you tap a small button centered on the end of the bottom bracket to engage and disengage the planetary gear. Three models are available: a "mountain gear" version that lowers whatever other gears you have by a factor of 2.5; a "speed gear" version that raises your other gears by 1.65x; and a "high-speed gear" version that raises your other gears by 2.5x. The Schlumpf drives have been marketed to specialty bicycles such as folding or recumbent bikes that use small diameter wheels, and thus can have difficulty getting "normal" gearing using off-the-shelf components. Schlumpfs have also been installed on unicycles which (obviously) are ordinarily a single fixed-gear.

An advantage of the Schlumpf drive is that with only one chain ring, there is no need for a front derailleur and the chain line is straight -- and one can tap the button to engage or disengage the drive even while stopped. However, despite the straight chain the Schlumpf drive appears to be less efficient in terms of power transmission. Measurements suggest that the Schlumpf drives "cost" about 5% extra in drive train losses. Since conventional derailleur systems range from around 92% to 97% in transmission efficiency (see for example, the work of Kyle and Berto here), an additional 5% loss can be a considerable cost.

Pinion has brought an 18-speed gearbox to the market, the P1.18. It isn't a "true" bottom-bracket with internal gears as is the Schlumpf -- rather, the gearbox is in a separate housing attached next to the bottom bracket, and it is not an "after-market" solution that can be easily added onto an existing bike. The Pinion is intended for downhill or freeride bicycles that are purpose-built around the device.