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 8 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)