19th century European scholars ascribed Ramayan and Mahabharat as mere figments of imagination. Here are a few reasons to believe that this is actually a history.
Few incedents mentioned in MB have been verified by archeological excavations, thus confirming that MB recorded historical events.
- MB describes the journey of Balaram along the banks of Sarasvati, which had dried in some parts. [Shalya Parva] Archeology has proved that Saraswati flowed parallel to the Sindhu, from the Himalayas to the Arabian sea. By 3500 BCE, Saraswati did not reach the sea, and by 1900 BCE she had completely dried. 
- MB describes that Dwaraka submerged in the sea, 36 years after the war. [Mausal Parva] A city was discovered by the team of Dr S. R. Rao submerged in the sea, near the current city of Dwaraka in Gujarat. 
- From the archeological discoveries at submerged Dwaraka it is concluded that: Dwaraka was built on reclaimed land. It displayed well organized six sectors, wide roads, residential and commercial zones, meeting halls and an excellent sea port. This is exactly how the MB describes Dwaraka. 
- The Matsya and Vayu Puranas describe great flooding which destroyed the capital city of Hastinapur. Then Nichakshu, 8th in line after Arjun, was ruling Hastinapur. Due to the floods, he relocated to Kausambi. The soil of Hastinapur reveals the proof of this flooding. 
- Excavations at Kurukshetra have yielded numerous iron arrow and spearheads, dated 2800 BCE (by Thermoluminence). MB describes that the great war took place at Kurukeshtra. 
- Not just Kurukeshtra, Hastinapur and Dwaraka, but 35 cities mentioned in MB, have been excavated. Prooving the existence of these cities and the historicity of MB.
- Chandogya Upanishad [3.17.6 ] mentions that Sage Angiras taught of soul's immortality to Devaki's son Krushn. And, this is what Krushn taught Arjun in Geeta. [Bheeshm Parva]
- MB mentions that Shantanu's brother Devapi renounced the kingdom and became a sage. [Adi Parva] Rg records that, Sage Devapi composed the rain hymn [10/98] of the Rg Veda when a terrible drought occurred in Shantanu’s kingdom.
- In MB, a sage tells Yudhishthir about the exile of the earlier king Ram and Sita. [Van Parva] Earlier text Valmiki's Ramayan, describes the exile of Ram, and his victory over Lankan king Ravan.
- The texts (Ramayan, Mahabharat, Puraan) record common dynasties, incedents, and people. No two novels would have the same incedents, same people or same dynasties unless they are recording history. 
- The Vedas were composed first, then the MB and then the Puraans. The past incedents in MB are recorded in the Vedas as present. The past recorded in the Puraans is recorded as present in MB. This continuity among the texts proves that the texts are historical recordings.
- MB records the king Bharat (son of Dushyant & Shakuntala), after whom the country is named Bhaarat. A country would not be named after the hero of a novel. (At least not the side-hero.) He has to be a historical figure.  Same for: Krushna and Bheema, the rivers named after Krushn and Bheem of MB. Dimapur (originally Hidimbapur) named after Hidimba, Bheem's wife.
- The time and place of events have been accurately recorded. All such recordings are redudant for a Maha-kavya. 
- The details of the weapons, and war are given to such a minute detail, that it gets boring for someone who would want to read a story. 
- A number of dynasties with their long lineage of kings (more than 50 from Manu) have been presented in Mahabharat. Information about important kings is given in detail. Their wives and their sons other important relatives are also recorded. If it were just fiction, 4-5 kings would have sufficed to build the story on. 
- Maurya, Gupta and Indo-Greek dynasties, are also recorded in our Puraanas. These dynasties are accepted as historical facts only because, they are also recorded by Greek historians. If the Puraans are correct about the later dynasties, they must be correct about the earlier dynasties that existed before the Greek historians.
- It stated in MB that the work is itihas [Adi Parva and Bheeshm Parva]. If the intentions of the writer were to write a poem, he would have stated it to be a "mahakavya" or "katha".
- MB describes that, Vyasa decided to write the itihas before the initiation of the war. He started writing MB after the death of Dhruturashtra and it took him three years to complete the work. Such recordings as when the author decided to write a novel / how long did it take him to complete it / the fact that he started to write it after the death of a novel character .... is unknown.
- MB records the astronomical events that happened during those times: like Krushna left for peace talks on Revati, Balaram left for pilgrimage on Pushya, the 13 day fortnight during the war, or Bheeshma died on Magh Shuddha Ashtami, which also happened to be the Uttarayan, the occurence of eclipses during the war, the position of the planets before and after the war etc. Such details can only be the observations on the particular days and not something that is woven.
- Lasty, why should we NOT believe in our ancestors? And why should we believe in the 19th century Christian scholars whose aim was to convert Hindus to Christainity?
- A new date for the Rg Veda - Dr. Nicholas Kazanas
- Myth of Aryan Invaion - David Frawley
- The legend of Dwaraka - T.R. Gopaalakrushnan
- Krishna Archeology - Nanditha Krishna
- Swayambhu - P V Vartak