Venice has the advantage of sparing most visitors the bother and expense of car hire: the streets, after all, are full of water. The exception to this is the Lido, where there are roads but they don't go very far, and finding somewhere to park your vehicle can be difficult.
If you arrive in Venice by car, you'll need to deposit it in one of the city's massive car parks. If you wish to take your car to the Lido, I explain how to do it on my How to get around Venice page.
If you're dividing your holiday between La Serenissima and a visit to the Veneto region, then hiring a car may prove convenient. Major centres such as Padua, Verona, Vicenza and Treviso are easily accessible by train from Venice. Resorts in the Dolomite mountains (www.infodolomiti.it) are rather more difficult to reach, however, and trying to visit Palladio's magnificent villas (www.palladiocard.it) scattered around the Veneto countryside is a nightmare without your own transport.
There are offices of most of the larger car-hire companies at all of the region's airports: Venice (www.veniceairport.it), Treviso (www.trevisoairport.it) and Verona (www.aeroportoverona.it). The airport websites list the companies present in their arrivals halls. Turning up without a car already booked is very risky, especially at peak periods. You may find you get a better deal from hire-car bureaux in city centres rather than at airports, though this, obviously, will mean dragging your luggage into town before you can get comfortably behind the wheel.