With proper nouns, we don't use the except for river names, newspaper names, etc.
I want to know why we use the with White House. I mean, under which rule can we categorize it? What could other similar examples for that rule be?
In general, we tend to use the as an article for nouns and proper nouns where it is clear from context that only one thing belongs to that description (or when we are talking about the archetypal thing of a set of things in the abstract). Otherwise we would normally use a to signify that we mean a single element out of a group of things that all fit the description.
The President of the United States is Barack Obama.
There is only one sitting US President, so the is the correct article to use here, but...
President Obama is a Democratic President.
There is more than one President from the Democratic Party, so a fits better here.
The most populous country is China.
*We use the here because there is only one "most populous country"*.
The President lives in the White House
Although there are many houses that are white, and there are even several copies of the famous White House, the context here makes it pretty clear which one we're talking about, and there's no ambiguity. Similarly it is clear which President we are talking about from context, and there's only one that fits the context.
This isn't even limited to proper nouns:
I'm going to turn on the TV
Although there are many TVs in the world, it is clear from context which one I mean.
I am looking forward to the launch of the PlayStation 4
*The second the here is talking about the singular product called "PlayStation 4", of which there is one (even though there are many units that will be sold), and the first the refers to the singular event which is the launch of that product*.
I own a PlayStation 3
Since I own only one of many PlayStation3 units
Here are some rules of thumb that will help you get by.
I came first in the pie-making contest!
(X) I came a first in the pie-making contest!
(X) I came the first in the pie-making contest!
Here are six apples.
(X) Here are a six apples.
(X) Here are the six apples.
Unless you are specifically referring to this group, which should be clear from context:
Here are the six apples [that we were talking about earlier].
2: Avoid putting adjectives on noun-phrases with omitted articles, but if you do prefix with an adjective, the article must be reintroduced:
Buckingham Palace is world-famous!
We visited the world-famous Buckingham Palace yesterday!
Except when talking about countries:
Join us on our exciting tour of historic China!
3: Never omit an article if the noun-phrase contains of:
The British Parliament sits in the Palace of Westminster.
The British parliament sits in Westminster Palace.
4: Always omit articles when talking about people by name.
(X) I love the Oprah Winfrey.
I love Oprah Winfrey.
But not, if the name of the individual is just part of a noun-phrase that isn't a person:
I love the Oprah Winfrey show
(X) I love Oprah Winfrey show
5: Omit articles when talking about companies by name or the buildings named after them.
She works at Microsoft.
(X) She works at a Microsoft.
(X) She works at the Microsoft.
When there are many places that share the same company name (e.g. McDonalds, Starbucks), then you can either omit the article, or use a. You can also always use the when talking about a specific place that is clear from context.
I work at Starbucks. (good)
(X) I work at the Starbucks. (not acceptable without context).
I work at the Starbucks [that we were talking about before].
I work at a Starbucks. (acceptable).
6: When talking about the singular names of most continents, territories, islands, settlements (including cities, towns, ports, villages, forts, and garrisons), states, lakes, waterfalls, bays, mountains, languages, sports, academic subjects, or street names we omit the article:
I visited London, which is in Europe.
(X) I visited the London last year.
We went to the Himalayas to climb Everest!
We'll meet at the top of Victoria Street and then we'll go to Brixton later.
The Great Lakes is a collection of lakes, so has an article.
But there are exceptions that must be learned by rote, such as
The International Criminal Court is based in the Hague.
I grew up in the Bronx.
7: We usually omit the article when talking about countries:
Some countries omit the, some don't. By default, the article is omitted, but it is reintroduced if:
The United States, the US (but not America), The United Kingdom, the UK (but not Great Britain, England etc), the USSR (but not Russia), The United Arab Emirates
The Azores, the Canaries, the Falklands, the Galapagos, the Bahamas, the Dao Yu Islands
The Philippines, the Netherlands.
The Russian Federation, The British Empire, The Roman Empire.
The People's Republic of China (but "I visited China")
The Islamic Republic of Iran (but "Iran is a beautiful country").
And there are a whole bunch of random exceptions:
The Vatican has an article, but Vatican City doesn't.
The Gambia uses an article, although it is sometimes used without one.
The Democratic Republic of the Congo is often (unofficially) called "The Congo".
Before 1991, Ukraine was referred to as the Ukraine (short for "the Ukrainian Soviet Socialist Republic"), but now has no article. In the mid 20th Century, "The Argentine" became known as Argentina.
We used to say "The Lebanon" (from the literal translation of HaLevanon), but now "Lebanon" is normally given with no article.
8: Some nouns are used without articles to indicate that they are being used in idiomatic form:
She went to bed (means she went to her bed in order to sleep)
She went to work (she went to her workplace to perform her job).
She went to school/university/college (means she attended her school. Also variants such as Summer school and Sunday school can be used this way.)
She went to church (means she attended church. Other religious places cannot be used this way. Articles are normally used for "He went to the temple/cathedral/mosque/synagogue etc")
She went to war (means she went to fight as part of the military abroad).
She went to prison/jail (means she was convicted of a crime, and was incarcerated).
She went to hospital (she was admitted to hospital. esp. British English).
She went to court (she was brought before a judicial court, either as the plaintiff or as the defendant, or possibly as a lawyer or judge presiding).
These nouns can be used with articles when the idiomatic form is not wanted and we want to refer to the noun in it's "ordinary" form:
The bed is broken.
The church is next to the synagogue.
The war in Iraq started in 2003.
I went to the prison in order to better understand the psyche of the inmates. (as opposed to I went to prison in order to..., which would imply that the speaker was incarcerated, rather than just visited).
I went to the hospital on Tuesday to pick up Auntie May.
These forms just need to be learnt.
9: Most names which are constructed from a possessive form of a person, city, county or suburb drop the article.
We visited Beeston Castle the other day!
Nelson's Column is 169 ft 3 in tall!
Queen Elizabeth I is buried at Westminster Abbey.
Kensington Gardens are very famous.
Seattle Tower is more commonly known as "The Space Needle".
Munich Cathedral is very impressive.
I'm writing a letter to Westminster City Council.
Sydney Opera house is amazing!
We visited St. Paul's Cathedral on Tuesday.
The Science Museum and the Natural History Museum are right next to each other.
The Tate Modern is quite expensive, but well worth the trip.
The British Library is free.
10: Nouns which are personal qualities are usually given with no article (see StoneyB's answer here)
He certainly has talent. (He is talented)
Nobody denies her courage. (She is courageous)
Sartorius lacks generosity. (Sartorius is not generous)
11: Most other nouns take an article, and the ones that don't tend to inconsistently have their articles used or not used by native speakers, so don't worry too much about them, and learn them by rote as and when they come up.
The Wikipedia article on Hagia Sophia uses the article "the" for Hagia Sophia 23 times but omits it 22 times.
"Taj Mahal" normally takes an article, but the official website uses both forms.
The Washington Monument / The Lincoln Memorial normally (but do not always) take articles.
(X) Signifies poor usage.
Sometimes there is no fixed rule. The Purdue OWL gives some guidelines about "Geographical" uses, but it doesn't say much about buildings and landmarks. However, the White House isn't the only building that uses the definite article; that practice seems to be rather common:
Sometimes the article seems to be optional:
Matt has covered it very well. Let me just add:
Don't get caught up on the fact that "White House" could be read as a description, that is, a house that is white. There are many words and phrases out there that have a general meaning, but that become proper names in one particular context. When we say "The president lives in the White House", we don't mean simply that he lives in some house that happens to be white, but rather that he lives in a particular building which is called by the name "White House". Similarly, if I say, "General Jones works in the Pentagon", I am not using the word "pentagon" in its general meaning as a geometrical shape, but rather to a particular building that is called by this name. I live near the Great Lakes. I'm sure there are many other lakes in the world that are great, but these particular lakes are named "the Great Lakes". This isn't limited to place names. There might be many companies in Britain that do something related to broadcasting, but if I say "the British Broadcasting Company" I am referring to one particular company that goes by that name. Etc.
As I understand it, there are two possible rules that can lead to this "the" before the phrase "White House".
When the speaker/writer believes that the hearer/reader knows exactly what he is referring to, e.g:
The White House is white. Both the speaker and the reader know exactly which "White House" the speaker is talking about.
When there is only one thing referred by "the". Such as
The 44th president of America and by extension
The White House. I'm guessing there is only one White House on this planet.
There is another usage worth mentioning here. Sometimes we use "the" not because there is only one thing we could be talking about, but because we want to emphasize that the one we're talking about is the one that is familiar to everyone.
For example, if I'm introduced to somebody named Brian Wilson, I might ask, "Are you the Brian Wilson?", with emphasis on the. I'm asking if he is indeed the singer from the Beach Boys, and not some other not-so-famous person who is also named Brian Wilson.
(Half of my question is answered by Safira and half by Matt, so I can't accept either of the answers. I am collaborating both the answers here so that I can accept one answer to my question.)
Rule: Out of similar things, if one is exceptionally well recognized, we use the determiner the with it.
There are many white houses, but the one that belongs to the US President is second to none in popularity. So, the White House.
Each planet has moon(s). But the one we see every night is the earth's only natural moon. So, the moon.
Each solar system has sun(s) (the star(s) around which planets move). But we are normally interested in the star that gives us light during the day. So, the sun.