Does placing a lid on a pot affect the rate of boiling? On the subject of cooking, someone once told me "If you have too much water in your pot after cooking a dish, just turn up the heat and let it boil without a lid for a few minutes".
Now I've thought about this, and as far as I can tell, it shouldn't matter if there is a lid or not.  In both situations the pot will stay at the same temperature (around 100 degrees Celsius), and therefore the amount of heat energy entering the pot will be the same.  The lid may cause some drops of water to condense and fall back in, but then it also traps heat and results in a higher rate of boiling inside the pot -- but the amount of water exiting the pot as vapour shouldn't change.
So by that reasoning it seems that it doesn't matter.  Or does it?
EDIT: Please note, I'm not talking about the time it takes for the water to reach its boiling point; I'm talking about the rate of water vapor leaving the pot when it is boiling.
 A: When cooking, keeping the lid on a pot does a few things if you think about it:   


*

*it decreases air circulation significantly so the air in the pot stays hotter, this cooks the food faster.

*if it's snug, it should increase the air pressure.*

*The pot lid captures condensation, so it will return water back into what you're cooking. That is, I think, the largest effect. 


I can't prove that with science, it's just my observation.   I cook a lot.    Often when I lift a lid off a stew or broth, the lid is wet and dripping.    Curiously, what this means is that water will get to a boil faster with the lid on, but it will boil away faster with the lid off.
* On Air pressure: I have a hard time believing that, unless it's a pressure cooker, this would be a significant increase, as air pressure is 14.4 lbs per square inch and what does the average lid weigh - a pound?    But there might also be a small decrease in pressure (er, I think), similar to Bernouli's paper lift. 
The boiling of water creates a wind direction of sorts off what you're cooing up through the pot and that wind direction should decrease air pressure, but that effect would likely also be small. Perhaps, the boiling point - no lid might be 98 degrees C and with lid, 101 degrees C - that's a guesstimate, but it shouldn't be a huge difference I would think.
A: This is the sort of question which is easily answered by actually doing the activity in question instead of looking at it and scratching your head.  And when you actually do heat the water you will find that yes, the time to get from room temperature (for example) to boiling is shorter with the lid on the pot - and noticeably shorter - than without.
Also, when you do this with a lid on which is not a snug fit but rather the sort of lid which just rests on the rim of the pan, you will see how much easier it is to spin the pan lid when the water is boiling.  During boiling you will see (and hear) the lid rattling as it rises very slightly and falls back.  The steam does mechanical work to lift the lid.  Now checkout James Watt.
A: The trick is here in the temperature of the pot.
As you know, evaporation does not require boiling at 100°C: else, towels would only dry in an oven, and as far as I know, nobody dries towels in their ovens. Instead, it depends on the partial pressure of water vapor near the water surface (as Hot Licks mentioned). 


*

*If the lid is on the pot, the partial pressure of water vapor under the lid is about equal to atmospheric pressure (slightly higher).

*If the lid is removed, the partial pressure of water vapor above the water is by approximation equal to the partial pressure in your kitchen (especially if you have a steady stream of 'fresh' air).

*With a lower partial water vapor pressure, the liquid will start evaporating more readily. This will lower the temperature of the evaporated water significantly: the enthalpy of evaporation is orders of magnitude more than the heat capacity of water!

*With a lower temperature, both heat losses due to convection and evaporation at the walls of the pan will lessen, and the heat source will be able to transfer heat more efficiently. 


So basically, with a lid, evaporation is a  'last resort' of keeping the water at 100°C, if 'normal' heat loss can't handle all of the incoming heat; without a lid, evaporation becomes the main way of losing incoming heat.
Although, of course, I challenge the OP to verify this with experiment, which is after all the core of science. Who knows this is just an urban legend, and your water will evaporate faster with a lid?
A: 
On the subject of cooking, someone once told me "If you have too much water in your pot after cooking a dish, just turn up the heat and let it boil without a lid for a few minutes".

That acquaintance was absolutely correct. There are a number of ways to cheat and quickly thicken a sauce, but (a) this is cheating, and (b) the sauce doesn't taste as good. Reducing the sauce is what the best cooks do.
Knowing when and when not to (and how and how not to) use a lid is Cooking 101. Presumably you can cook rice. You would never cook rice without a lid, would you? (Actually, you can cook rice without a lid, but this is beyond Cooking 101.)
Knowing how to properly reduce a sauce is just a bit beyond Cooking 101. Basically, you turn the heat up and you stir. Stir frequently.

So by that reasoning it seems that it doesn't matter. Or does it?

By way of analogy, suppose you go to a hotel or visit a friend in the far north that seems to think 60 Fahrenheit (15 Celsius) makes for a nice comfy sleeping temperature. Are you going to use a blanket, or say that it doesn't matter and sleep commando? Or does it? That's a rhetorical question. Of course it matters.
It matters even more with cooking.
Update
The reason using a lid (or not) matters more with cooking is twofold. I'll look at this in the context of the question raised in the title of the thread,

Does placing a lid on a pot affect the rate of boiling?

Note well: This is the wrong question with regard to the body of the question. I'll get to that later. The answer to the question raised in the title of the question is "yes".
Some of the answers have posited that the lid raises the boiling point. This effect is marginal. The Clausius-Clapeyron equation describes the relation between pressure, temperature, and the vaporization pressure of a liquid:
$$\frac{d\ln p}{dT} = \frac {\Delta H_\text{vap}}{RT^2}$$
At sea level, water boils at 373.15 K and has a heat of evaporation of 40.657 kJ/mole at that temperature. Linearizing the Clausius-Clapeyron equation yields a 0.2848 kelvin increase in the boiling point for each one percent increase in pressure. Unless one is using a lid that is held down with clamps, this is a small effect. A hefty lid might raise the pressure inside the pot by a few fractions of a percent. This is at best a small secondary effect of using a lid.
The primary effects of using a lid are to drastically reduce convective heat transfer from the steam/vapor to the atmosphere and to drastically reduce vaporization of the water. All other things being equal (same pot, same heat setting, same amount of water), a boiling pot of water covered with a lid will have a higher boiling rate than will an uncovered boiling pot of water. Some of the heat supplied to the uncovered pot goes toward countering the increased heat transfer rate due to vaporization and convection.
You can see this effect if you have pots with glass lids. Cover the pot, bring some water to a vigorous boil, and take the lid off. The boiling rate will decrease once the lid is removed. If you reduce the heat to a low simmer before taking the lid off the effect is even more dramatic: The water stops boiling. Yet another way to see these effects is to time how long it takes for a covered versus uncovered pot of water to come to a boil.
I mentioned above that this is the wrong question. The advice given to the questioner was not about the boiling rate. It was about increasing the evaporation rate for a dish that has a bit of excess liquid at the end of cooking. Presumably the advice was for a dish cooked at a low simmer. Very little water vapor escapes the pot or pan while covered. Most of the water vapor created by simmering instead condenses on the inside of the lid and soon rejoins the dish. The gas underneath the lid is mostly water vapor at close to the boiling point. There is very little evaporation from the food.
Removing the lid exposes the cooking food to air at a much lower absolute humidity. The entire surface evaporates, and the vapor is quickly carried away. Assuming no change in the temperature control, the rate at which water escapes increases significantly even though the boiling rate has decreased.
Note that the exact same advice given to the questioner was given here at the cooking stackexchange site.
A: If you want to get technical, check out steam tables such as found on:http://www.engineeringtoolbox.com/saturated-steam-properties-d_273.html
Putting the lid on the pot will slightly raise the pressure inside the pot, therefore the boiling point will raised. The steam generated will be under somewhat higher pressure. When this happens the latent heat required to generate a pound of steam will go down. This means that you will actually generate more lbs of steam with the same amount of heat at the boiling point. But it will take more heat to raise the temperature of the water to the boiling point which offsets the lower latent heat requirement. So it would seem that you would actually generate less steam with the lid on, unless you raise the pressure and temperature extremely high, then things change drastically. But that is another subject.
With normal pots, I think any differences are negligible. Pressure cookers on the other hand cook foods faster because of the higher temperature (boiling point) inside the pot. Of course, when the temperature inside the pot is higher, less heat will enter the pot because of the smaller temperature difference between flame ant pot.
Also, I am told you should never watch a pot or it will not boil. 
