The answer, most of the times, is yes.
If you are going to Sardinia for a short city break of two or three days in Cagliari or Alghero, then you probably do not need it.
The airports are not too far from the towns and you can easily get a cab from there. You can visit the city centre by foot and you can reach the local beaches by bus, even if the public transport can be a little bit slow…
If you are planning a tour of different areas of Sardinia also taking many day excursions or visiting the most secluded areas of the island, then you really need to hire a car.
Top tips:
1) Sardinian drivers are very “creative”, as Luca says, so be careful

2) Directions are not always good, so check your route on a recent maps before you start going.

Ciao

Manu