If you are just making a short visit the rock itself, then there is clearly no need to hire a car as it is easy to walk both around Gibraltar itself and to walk from the airport to any part of the peninsula. However, for anything longer than a day or two, then you will want to head into Spain, and a hire car is going to make this a great deal easier, despite the hassles of crossing the border, however you choose to do it.
Should you rent a car in Gibraltar? Based on Gibraltar being so poorly connected to Andalusia by public transport, and Gibraltar Airport car hire prices being very reasonable compared with nearby Spanish cities, you will certainly be much better off with a hire car. However, there are various interesting options to explore both the rock and beyond by everything from cable car to boat to scenic train from slightly further afield – or indeed in a different continent! Therefore, even though a car is useful, with a bit of planning, it is perfectly easy to get by without a car.
VERDICT: YES (a car is extemely useful for driving into Spain but not essential)