1 Canada Square
This is the one that's often erroneously referred to as "Canary Wharf Tower".
Identifiable from a great distance as a pencil shaped tower with a flashing light on top (for aircraft), this building is a monument to 1980s style capitalism. It is currently London's tallest building, and there seems to be no likelihood that a larger one will be approved any time soon.
It is not possible for members of the public to go up the tower. There are a large number of distinct businesses operating from inside the tower, including a number of newspapers (including the Independent and the Mirror). The ground and basement stories of the tower are a shopping centre, which have a tunnel connecting with the Jubilee Line station. It is possible to walk from the DLR station to the tube station without going outdoors; there's signing to this effect.
The building now has two siblings that have sprung up alongside, which are not quite as tall (at 200 metres each, to 1 Canada Square's 240 metres; it's the pyramid that does it).
- HSBC tower (8-16 Canada Square)
- Citigroup tower (25 Canada Square)
More on this tower at http://www.skyscrapers.com/english/worldmap/building/0.9/110714/index.html