MB is a milestone in the history of India. The next milestone is the era of Buddha and Mahavir, which again defines a new age for Bharat. Adi Shankar is believed to be about 1000 years later to Buddha. Hence the date for Adi Shankara is set to 800 CE. If the date for Buddha is moved, the dates for Adi Shankara, Ajatshartu, Shishunga Dynasty, Maurya dynasty etc. also move. Similarly, many ancient events like the end of Vedic age, the start of Kali, the dates for Upanishadas, the dates for the pre-mauryan dynasties etc. are related to the date of MB. Hence fixing the date for MB is important for the history of India. Different dates have been proposed ranging from 5500 BCE to 900 BCE. Following is a brief summary of this research:
MB Date by Puraan
Genealogies of different dynasties are recorded in the Puraan. Knowing the date for Maurya Dynasty as 323 BCE, and the list of pre-Mauryan dynasties from the Puraan, the date for the great war comes to 1924 BCE1
Among the genealogies, Ikshvaku line is the longest, with 93 kings from Manu to Bruhadbala of MB. For the same period it gives 53 kings from Manu to Dhruturashtra. Obviously the Kuru line is not complete. Even the Ikshvaku line need not contain ALL the kings of that line.
Generally only the prominent kings get mentioned in the genealogies. This is also proved by the fact that, the kings like Sudas, Divodasa, Somaka, etc. are mentioned in Rg Ved, but not in the Puran. As the Puranic genealogies are far from complete, the date of 1924 BCE is the lower limit for the MB date.
Date according to Kali Yug
In 500 CE, Aryabhatta calculated the start of Kali Yug as 17th February, 3102 BCE. This is based on the position of planets at the start of Kali Yug. By tradition, the Kali Yug started with the death of Krishna, 36 years after the War. Therefore it is thought that the Mahabharata War took place in 3137 BCE.
Modern studies prove that a conjunction of the planets did occurred on Feb 17, 3102 BC. (By tradition, a conjunction of Saturn, Jupiter, Mars, Venus, Mercury, Sun, Moon and Ketu (southern lunar node) near Revati occured at the start of Kali.) Thus the traditional date of 3137 BCE could be a possible date for the war.
The famous Aihole inscription of Chalukya King Pulkeshi II says: the temple was constructed 3735 years, after the Bharat War. This inscription was written in 634 CE. Thus the date of the MB war by this inscription is 3102 BCE. This inscription was written too long after the MB war, and hence this is not given much credence.
Date according to the Western Indologists of 19th century
A date of 900 BCE was proposed by the western Indologists. This date was calculated according to the Bible chronology, which assumed that the Earth was created in 4000 BCE. To fit the long history of India in this time frame, required MB to occur no earlier than 900 BCE. Now that the science has proved that the Earth and Homo sapiens were created long before 4000 BCE, this date of 900 BCE should be discarded. (I am writing "should" because it is not yet discarded from the history text books.)
Dwarka: Dr S R Rao who carried out the under water archeology expedition assigns a date of 1800 BCE to Dwaraka.  The work is still incomplete and more excavations at Bet Dwaraka are yet to be carried out, leaving a possibility of finding earlier remains.
Kurukshetra: At the scene of the great Mahabharata war, iron arrows and spearheads have been excavated and dated to 2800 BCE. (Thermoluminence) 
Hastinapur: Iron objects including arrows, spearheads, shafts, tongs, axes and knives indicate the existence of a vigorous industry. There are indications of brick-lined roads and drainage systems, and an agro-livestock based economy. The PGW of Hastinapura has been assigned to 1100-800 BCE. But according to Kak, this date need not be corelated to the Kaurav. 
Saraswati: Recent archaeological discoveries indicate that the Sarasvati river ceased to be a sea flowing river by 3500 BCE, and had dried up around 1900 BCE.  Balaram's pilgrimage along the banks of Sarasvati is described in MB. Thus the MB war cannot be dated later than 1900 BCE.
An Egyptian Pyramid, dated 3000 BCE, has the following verse from the Bhagavad Geeta:
vasanvsi jeernani yatha vihaya, navani
ghrunnati naro parani
- Nava Bharat Times, 18-4-1967 
Dion Chrysostom, Greek Sophist writes in 100 CE, that the Indians possess an Iliad of 100,000 verses. Together with its appendix, the Harivamsha, MB does add up to this total. Thus the MB, of the current volume was complete by 100 CE.
Panini's grammar (500 BCE, a most conservative date) knows the Mahabharata. The language of the Epic does not always follow Paninian constructions, which also suggests that it is prior to Panini.
The epic does not mention Buddhism, so we can be certain that it was substantially complete prior to Buddha, i.e. 500 BCE.
The Brihadaranyaka Upanishad remembers a line of 60 teachers. This line could span at least a thousand years. This Upanishad dates to 800 BCE (most conservative date) The Rg Veda was complete before this Brihadaranyaka Upanishad. Thus Rg Veda and hence the MB war too, cannot be dated later than 1800 BCE. 
Recent archaeological discoveries indicate that the Sarasvati river ceased to be a sea flowing river by 3500 BCE, and had dried up around 1900 BCE. The older portions of Rg Ved, extol the river as the naditame best river that flows from mountains to the sea. This portion cannot be dated later than 3800 BCE. The latest book X of Rg Ved only mentions Sarasvati among the list of rivers. This is attributed to a date later than 3500 BCE and before 1900 BCE.  The Rg Veda and hence the MB war too, cannot be dated later than 1900 BCE.
From astronomical evidence in the texts later than Rg Ved, such as Shatapath Brahmana or the Taittiriya Brahmana: the Brahmana's are assigned a date of 2900 BCE. Thus the compilation of the Rg Ved and hence the MB war must have taken place before 2900 BCE. 
Date according to Astronomy:
Astronomical events mentioned in MB are used to calculate the date of the MB War. One such event is the death of Bheeshma on a winter solstice day, Magh Shukla Ashtami. From this date one calculates the date of MB as follows:
The axis of the earth is tilted to the ecliptic (the plane in which the Earth revolves around the sun) by 23.5 deg. For an observer on the Earth, it appears as if the Sun is in the North in summer, and in the South in winter. Throughout the year, the Sun apparently travels from North to South and back. Winter solstice is the day when the Sun starts the journey back to North (Dec 21/22).
Due to the gravitational forces exerted by the sun, moon and the planets, the axis of the Earth wobbles. (like that of a spinning top.) The axis undergoes a slow conical clockwise motion with a period of 26,000 years. Because of this the winter solstice moves earlier each year. (About 1 degree per 72 years.)
More than 4000 years ago, the celebration2 of Uttarayana (Winter Solstice) started in India. In those times, this day was 14 Jan (Makar Sankrant). Even now, Uttarayana is celebrated on Jan 14, throughout India. Though Bheeshm died on the Winter Solstice day, the celebration of Uttarayana is not mentioned in the MB. Thus Bheeshma must have died before 2582 BCE. This is the lower date for MB war.
Other astronomical events mentioned in MB are also used to calculate the date for MB. MB mentions a lunar eclipse followed by a solar eclipse in 13 days. Using this data, Dr S Balakrishna calculates the MB date to be either 3129 BCE or 2559 BCE. 
The archeological evidence points to a date between 3500 BCE and 1800 BCE. However there are some difficulties with the Archeological data gathering. India being a hot and a humid country the remains are not well preserved. Secondly Hindus did not bury their dead like the Egyptians, for archeologists to dig out graves and the buried artifacts. Thirdly, Bharata has been continuously densely populated for thousands of years. Archeological evidence is difficult to come by because many 100’s of generations of people are living in same area.  Also, the dates assigned to different MB sites are not consistent with each other. The archeological excavations are incomplete, and more extensive diggings would be required for a solid proof for the date of MB war.
Due to shortcomings of archeology, one has to rely on the evidence provided by the texts. The traditional date of 3100 BCE is supported by the literature, archeo-astronomy, and Aihole inscription. Thus 3100 BCE seems to be the most probable date for Mahabharata.
On Chronological framework for Indian culture - Subhash Kak
The date of Mahabharata war - Subhash Kak
The date of Mahabharata War with reference to Bhishmashtami - Dr S Kalyanaraman
Legend of Dwaraka - The Week, June 2003 issue.
A new date for the Rg Veda - Dr. Nicholas Kazanas
Swayambhu - Dr P V Vartak
Mahabharata and Sindhu-Saraswati tradition - Subhash Kak
Dating of MB - Two eclipses in 13 days - Dr S Balkrishna
Krishna Archeology - Nanditha Krishna
Dynasty No of Kings No of Years Time
Brihadrath 32 kings 967 years 1924-957 BCE
Pradyot 5 kings 173 years 957-784 BCE
Shishunag 10 kings 360 years 784-424 BCE
Nanda 9 kings 100 years 424-324 BCE
Maurya 9 kings 137 years 324-187 BCE
The journey of sun back to north is celebrated all over the northern hemisphere, in all societies. Even Christmas! Dec 25 was earlier celebrated as the "Uttarayana", and later as birthday of Chirst. December 25th was the date of the winter solstice in the calendar Julius Caesar devised for Rome in 46 BCE.
Prior to the fourth century, Christ’s birth had been associated with Three King’s Day on January 6. But the pagans and the newly converted were being a major problem to the Church because they were still celebrating the Unconquered Sun. Nothing the Church did or said made a difference; the winter solstice was just too important a festival. Since the Church could not defeat them, they made it appear as if it had. Sometime around 360 CE the celebration of Christmas was shifted to the day of the Unconquered Sun - Dec 25!