Why is there water coming out of a car’s tail pipe? I notice yesterday that my neighbor’s car had water coming out of the exhaust pipe in the morning. My first response was since the hot exhaust is hotter than the cold tail pipe, heat is transferred from the hot exhaust through the pipe, and with enough moisture in the exhaust, enough heat leaves such that the humid air is condensed forming water drops. 


*

*Is my thinking correct here? If not, please correct me.

*Does the water come from (i) a chemical byproduct of gasoline combustion or (ii) the humidity of the air (i.e. I've only noticed this in the winter, not the summer so I assume that during the summer this would not happen since the tail pipe is “already warm enough.”)

 A: It can't be from the moisture in the air. If there was enough moisture in the air to produce condensation then it would be condensing on everything. There would actually be less of it condensing on the tailpipe, because the tailpipe is quite warm.
In fact the water is generated by the combustion of the fuel in the car. It comes from the hydrogen in the fuel, plus some of the oxygen from the air. For example, the combustion of octane is
$$
\mathrm{2C_8H_{18}+25O_2 \to 16CO_2 + 18H_2O + \text{heat}}.
$$
This is just the net result of an extremely complex series of reactions, and motor fuel is not just octane, but ultimately burning fuel in a car will produce carbon dioxide and water in roughly equal amounts, plus much smaller amounts of a whole bunch of other things.
Usually the $\mathrm{H_2O}$ will be in the form of water vapour, but if it's cold then this will condense, and this is the liquid water you see coming out of the tailpipe. 
A: Yes, your thinking is correct, and the water is a byproduct of combustion. Let's examine what happens.
Many combustion reactions involve reacting hydrocarbons with oxygen. Hydrocarbons are any molecule consisting of hydrogen, carbon, and sometimes oxygen. The byproducts of these are always CO2 and H20, so carbon dioxide and water, or the infamous dihydrogen monoxide. Notable hydrocarbons include butane (C4H10), propane (C3H8), and sugar (C6H12O6), which also is a large component of wood. Kerosene, diesel, and, as you asked about, petrol all involve different kinds mixes of hydrocarbon chains which change based on what season it is, what region you're in (if you're American) or, I'd imagine, what country you're in. 
A hydrocarbon combustion reaction looks like this (the lowercase letters are variables denoting the number of atoms in each molecule)
HxCyOz + O2 => H2O + CO2
Obviously this is not a balanced equation, and I'm sure you could do a bit of algebra to figure out what the balanced equation for any hydrocarbon, but I won't.
So the reason you're seeing water coming out of the tailpipe is that the petrol is combusting above 495 degrees F (I'd imagine this would be varying temperatures based on engine design, and according to the heat engine model, a hotter temperature engine is more efficient) and then cooling down as it leaves the pipe. Now the exhaust system is hot, don't get me wrong, but it's nowhere near as hot as the air coming out of the pistons, which is the source of the heat in the first place. 
Since the air coming out of the engine is fully saturated with moisture, any drop in temperature will cause the water to precipitate out. A cold winter's day is going to amplify this effect.
A: Gasoline is a hydrocarbon - the molecules contain hydrogen and carbon. When burned, they produce carbon dioxide and water. They are both gases when formed in the engine, but when the water vapour comes into contact with the cold exhaust pipe, it condenses, so you will see liquid water dripping out. After the car has run for a while, the exhaust pipe heats up to the point where the water vapour no longer condenses and the dripping stops.
By the way, it isn't plain water... some of that carbon dioxide will become dissolved in the water to form a dilute carbonic acid.
A: For the record, it might be a partially blown head gasket letting water flow from the coolant channels, into the combustion chambers, and out the exhaust.  A lot of water flowing out of the exhaust isn't normal.
A: I too was observing this problem for quite some time with my new car equipped with gasoline injection system instead of the earlier carburetor type. The water dripping from the tail pipe is observed when the car is taken for a short run and stopped.
Obviously, the hydrocarbon fuel (petrol) is oxidized more or less fully in the newer cars fitted with catalytic converters to CO2 and H2O. If the silencer is cold (as is the case when the car runs for a short distance) a good amount of the water vapor in the exhaust gets condensed and may remain in the recess of the silencer. This water would also absorb some CO2 to become mildly acidic and would cause corrosion of the silencer and the tail pipe. That is the reason why we need to change the silencers within a couple of years time unless it is made of stainless steel.  
