Very little, if any, especially when you look at it from the perspective that true Christianity is not a religion but a relationship with God.

Hinduism is based on duty and service while Christianity is based on a relationship that will never be severed.

Correspondences between events in Jesus' and Krishna's life: bullet #6 & 45: Yeshua and Krishna were called both a God and the Son of God. bullet 7: Both was sent from heaven to earth in the form of a man. bullet 8 & 46: Both were called Savior, and the second person of the Trinity. bullet 13, 15, 16 & 23: His adoptive human father was a carpenter. bullet 18: A spirit or ghost was their actual father. bullet 21: Krishna and Jesus were of royal descent. bullet 27 & 28: Both were visited at birth by wise men and shepherds, guided by a star. bullet 30 to 34: Angels in both cases issued a warning that the local dictator planned to kill the baby and had issued a decree for his assassination. The parents fled. Mary and Joseph stayed in Muturea; Krishna's parents stayed in Mathura. bullet 41 & 42: Both Yeshua and Krishna withdrew to the wilderness as adults, and fasted. bullet 56: Both were identified as "the seed of the woman bruising the serpent's head." bullet 58: Jesus was called "the lion of the tribe of Judah." Krishna was called "the lion of the tribe of Saki." bullet 60: Both claimed: "I am the Resurrection." bullet 64: Both referred to themselves having existed before their birth on earth. bullet 66: Both were "without sin." bullet 72: Both were god-men: being considered both human and divine. bullet 76, 77, & 78: They were both considered omniscient, omnipotent, and omnipresent. bullet 83, 84, & 85: Both performed many miracles, including the healing of disease. One of the first miracles that both performed was to make a leper whole. Each cured "all manner of diseases." bullet 86 & 87: Both cast out indwelling demons, and raised the dead. bullet 101: Both selected disciples to spread his teachings. bullet 109 to 112: Both were meek, and merciful. Both were criticized for associating with sinners. bullet 115: Both encountered a Gentile woman at a well. bullet 121 to 127: Both celebrated a last supper. Both forgave his enemies. bullet 128 to 131: Both descended into Hell, and were resurrected. Many people witnessed their ascensions into heaven. Points of similarity found by other writers: "The object of Krishna's birth was to bring about a victory of good over evil." 2 bullet Krishna "came onto earth to cleanse the sins of the human beings." 2 bullet "Krishna was born while his foster-father Nanda was in the city to pay his tax to the king." 3 Yeshua was born while his foster-father, Joseph, was in the city to be enumerated in a census so that "all the world could be taxed." bullet Jesus is recorded as saying: "if you had faith as a mustard seed you would say to the mountain uproot yourself and be cast into the ocean" Krishna is reported as having uprooted a small mountain. 4 bullet Krishna's "...foster-father Nanda had to journey to Mathura to pay his taxes" just as Jesus foster-father Joseph is recorded in the Gospel of Luke as having to go to Bethlehem to pay taxes. 10 bullet "The story about the birth of Elizabeth's son John (the Baptist), cousin of Jesus, corresponds with the story in the Krishna myth about the birth of the child of Nanda and his wife Yasoda." 10 Nanda was the foster-father of Krishna. bullet The Greek God Dionysos, Jesus and Krishna were all said to have been placed in a manger basket after birth. http://www.religioustolerance.org/chr_jckr1.htm French historian Alain Danielou had noticed as early as 1950 that “a great number of events which surround the birth of Christ - as it is related in the Gospels - strangely reminded us of Buddha’s and Krishna’s legends.” Danielou quotes as examples the structure of the Christian Church, which resembles that of the Buddhist Chaitya; the rigorous asceticism of certain early Christian sects, which reminds one of the asceticism of Jain and Buddhist saints; the veneration of relics, the usage of holy water, which is an Indian practice, and the word “Amen,” which comes from the Hindu (Sanskrit) “OM.” [...] There are many other similarities between Hinduism and Christianity, including the use of incense, sacred bread (prasadam), the different altars around churches (which recall the manifold deities in their niches inside Hindu temples), reciting prayers on the rosary (Vedic japamala), the Christian Trinity (the ancient Vedic trinity of Brahma, Vishnu and Shiva as the creator, maintainer and destroyer respectively, as well as Lord Krishna as the Supreme Lord, the all-pervading Brahman as the holy ghost, and Paramatma as the expansion or son of the Lord), Christian processions, and the use of the sign of the cross (anganyasa), and so many others. http://atheism.about.com/b/a/242056.htm