Vehicle

Mechanical vehicles, especially those running on petrol, are generally non existent in the Fallout universe. The most common means of transport are brahmin carts. The super mutant army is also said to have used some steam-powered trucks.

The war was fought mainly for resources. The last resources remaining were probably depleted in the war itself. Without resources, vehicles couldn't be driven anymore. Furthermore, it is generally accepted that after the war, much of the human knowledge was lost. The knowledge of how to tend to the high tech fusion cars that existed before the war was lost, and with it the necessary skills to repair the cars.

Fallout 1
There were no vehicles at all in Fallout 1 outside of the brahmin carts and a steam truck mentioned at one point in the game.

Fallout 2
Fallout 2 featured a fully working car, the Highwayman, and high tech flying machines, known as Vertibirds. It is also mentioned that the NCR military includes mechanized forces, though this could also refer to any soldiers equipped with Power Armor. Given the presence of car mechanics in NCR and a car chop-shop in New Reno, it is probable that some form of automobile was present in the NCR's mechanized units.

Fallout Tactics
Fallout Tactics featured many vehicles that the player could operate, causing yet another point of controversy that contributed to the opinion of Fallout Tactics being non-canon although the cars do not appear to actually use gas as there are no emissions of any kind. Also, Fallout Tactics is set in what is the heart land of the automotive industry, giving some argument to the plausible presence of functioning vehicles. The vehicles are also used exclusively by the Brotherhood of Steel, who would have the technical know-how to get vehicles functioning.

However, since there are still untouched reserves of pre-war tech (like the Sierra Army Depot), it is reasonable to assume that vehicles will continue to have a presence in the Fallout universe. If the Den is capable of keeping a fusion car from rotting, imagine what a more advanced town might have squirreled away.

Fallout 3
In Fallout 3, there are no drivable vehicles, although there are hundreds of highly explosive, derelict vehicles that will explode violently a short while after being damaged. When a vehicle explodes, the resulting explosion can cause other vehicles close to it to explode causing a deadly chain reaction. This particularly happens in drive-ins and on highways. There are also Enclave-controlled Vertibirds. They appear at Raven Rock and on random encounters occupied by squads of Enclave soldiers. In the Add on Broken Steel the player can visit the interior of the  Brotherhood of Steel's unique vertibird, which they have captured.

It is also conceivable that once civilization has recovered enough in a given area that vehicles beyond brahmin carts will appear. These vehicles could be restored pre-war machines or they could be some form of steam-powered machines.

Strangely, most vehicles appear to be run on radiation as most of them have an exhaust at the back (specifically buses) that say "Warning: Radiation" on them. However, it is not known if vehicles are run on just radiation or on petroleum with radiation as an additive. Although, they are probably fusion cars, since gas powered cars don't produce radiation and no other power sources are ever mentioned(fusion and gas), at least not in such numbers.

Van Buren
Van Buren, the canceled Fallout 3 by Black Isle Studios, featured many drivable vehicles including a train.