There are many definitions and ways to determinate biggest cities of the world. Here I took numbers of biggest agglomerations from this site. This list is based on population inside metro area of cities.
1. Tokyo - capital of Japan (population: 33,600,000). It is a destination for my dream travel, perhaps one day... 
Image credit: Yahoo
Tokyo originally was called Edo, the name of city was changed when it became of capital de facto of Japan in 1868. And the name means Eastern Capital. Tokyo was left twice in ruins by earthquake and bombarbement, because of this it is modern city with few old buildings left intact. In foto - beautiful Rainbow Bridge build in 1993, 570 meters long.
2. Seoul - the capital of South Korea (population: 23,400,000).
The city's current name - Seoul - means Capital City. City itslef has appeared in 18 BC. The heart of Seoul is old Joseon Dynasty city, where are situated most governent offices, palaces etc. In photo Gyeongbok Palace or Kyongbok Palace is a palace located in northern Seoul, South Korea. It was the main and largest palace of the Joseon Dynasty and one of the Five Grand Palaces built by the Joseon Dynasty.
3. Mexico City - capital of Mexico (popolation: 22,400,000).
by lreed7649
Mexico was fouinded as Mexico-Tenochtitlan on 18, 1325 by the Nahua Aztec. The famous sites are historical centre of the city, "floating gardens", and also Metropolian Chatedral (in photo).
4. New York (population: 21,900,000) in USA.
New York was born as Dutch fur trading settlement - New Amsterdam. In 1664 English conquered the city and renamed it New York. In ourdays New York is big culture center, famose with art galleries and theaters. The simbol of New York and whole America is Statue of Liberty (in photo) stands on Lyberty island. Statue's classical appearence derives from Libertas, ancient roman's goddess of freedom from slavery, oppression and tyranny.
5. Mumbai formely known as Bombay (popolation: 21,600,000) in India.
The city is very old. Artefacts found near Kandivali in northern Mumbai indicate that these islands had been inhabited since the Stone Age. Documented evidence of human habitation dates back to 250 BC, when it was known as Heptanesia. One of the monuments of Mumbai - Flora Fontain (in photo) was built in 1864. It represents roman goddess Flora and is now a heritage structure.
6. Delhi (popolation: 21,500,000) - India.
Wikipedia
Dheli
is one of the oldest cities in the world and has been a capital of
several empires. Today it is major economical and cultural centre of
India. Bahá'í House of Worship (in photo) known as Lotus Temple is a
prominent atraction of the city. It was constructed in 1986 and serves
as the Mother Temple of Indian subcontinet. It has also won numerous
architectoral awards.
7. Sao Paulo (popolation: 20,600,000) - Brazil.
Sao Paulo is the largest city in Brazil. The city was founded in 1554 by jesuit missionaries. Sao Paulo is a major cultural centre with diverse national infuences. It is famous for it's rich in variety cuisine. Sao Paulo Cathedral (in photo) - is a chatedral in ghotic style and one of the sights of the city.
8. Los Angeles (popolation: 18,000,000) - USA.
7. Sao Paulo (popolation: 20,600,000) - Brazil.
Sao Paulo is the largest city in Brazil. The city was founded in 1554 by jesuit missionaries. Sao Paulo is a major cultural centre with diverse national infuences. It is famous for it's rich in variety cuisine. Sao Paulo Cathedral (in photo) - is a chatedral in ghotic style and one of the sights of the city.
8. Los Angeles (popolation: 18,000,000) - USA.
Los Angeles was founded in 1781 by Spanish governor Felipe de Neve. Today Los Angeles is ther second largest city in USA and major world culture centre.Hollywood sigh (in photo) has become the simbol of the city in the whole world. It was build as an advertisement in 1923.
9. Shangai (popolation: 17,500,000)
Shangai is a largest city of China. A city wall has been buid in AD 1553 and this date is considerated as a foundation of Shangai. However, before the 19th century Shangai was not considered major city and therefore this is a modern city with little ancient landmarks. Jing'an Temple (in photo) is a buddhist temple and was build in 247 AD, during the Three Kingdoms period.
10. Osaka (popolation: 16,700,000) - Japan.
Some of the earliest signs of inhabitance in Osaka region was found at the Morinomiya ruins in dating 5 - 6th centuries BC. Odsaka literally means "large hill". Osaka castle (in photo) is one of the most famous castles in Japan. It played a major part in unification of Japan.
