Manipulator arm

The manipulator arm is the long, thin, mechanical arm usually found on most Dalek models, the exceptions being some Dalek Emperors' models and the Special Weapons Dalek-type model.

It is usually found in the right-hand socket in the Dalek mid-section, with the gunstick on the left, however some of the black-domed Daleks within the Dalek Imperial fleet in the year 200,100 had it the other way round. (DW: The Parting of the Ways)

Plunger
Manipulator arms typically have a shape like a plunger. For this reason, Dalek technology often has circular controls with which some an arm can interface by moving clockwise or anti-clockwise. However, the black tip at the end, which gives the arm its "plunger" shape can change into different shapes if needed (such as finding the combination of electronically locked doors). (DW: Dalek)

Even the Dalek dies, its arm can still operate machinery if used by a live person (DW: Remembrance of the Daleks). The arm can optionally can have a telescopic feature to enable the arm to extend outward. (DW: The Dalek Invasion of Earth)

It could also serve as a weapon. Placed over the nose and mouth, the arm can generate enough hydraulic suction to suffocate and kill a Human and enough to traction to more than crush a human skull or rip through sheet metal. (DW: Dalek, TDA: I am a Dalek)

At least in the case of the Cult of Skaro, the arm could also scan brainwaves for information or as a quick intelligence scan. (DW: Doomsday, Daleks in Manhattan)

Claw
Alternatively, the arm can terminate in a simple mechanical claw with two or three pincers. Another type of claw appeared in DW: The Stolen Earth, it had eight pincers and was used to operate Dalek machinery.

Combination
One of the members of the Cult of Skaro exhibited a combination of the two forms, as a plunger which also had a claw. The claw was in this case used to hold a syringe. (DW: Daleks in Manhattan)

Blowtorch
Some Daleks had a claw and blowtorch combination. (DW: The Parting of the Ways); (DW: The Daleks)

Alternative weapon
The alternative weapon which appeared in DW: The Parting of the Ways was only seen on two Daleks guarding the Dalek Emperor. It looked like an upgraded Dalek ray gun, but slightly larger. Also, in the stolen earth/journeys end, Davros' Crucible daleks had a door unlocker.