First of all, Polyvinylidene fluoride (PVDF).  In order to obtain a piezoelectric response, the material must first be poled in a large electric field.

I agree with Serge V. Shil'ko. PVDF is mostly considered as piezoelectric polymer.

These polymers are called electroactive polymers (EAP). Here are a few examples of EAPs:

Polyethylene,

Polyvinyl chloride(PVC)

Polyisobutylene

Polystyrene

Polycaprolactam (6-nylon)

Polyisoprene (natural rubber)

Hope this helps answer your question.

Professor Yehia Khalil, Yale University, USA

Fellow of the University of Oxford, UK

PVDF is the only polymer which is piezoelectric .

PVDF is most famous one. You can go this reference to find more: http://onlinelibrary.wiley.com/doi/10.1002/0471440264.pst427/abstract

There are many polymers that have piezoelectric properties.

Nylon, polyimide, teflon, others. None are as good as PVDF and its copolymers of TrFE by a factor of 10x or more.