http://www.breslov.org/aboutbreslov/quest2.html#1113. Some Breslover Chassidim travel to Rebbe Nachman's gravesite in Uman in the Ukraine. Why?
Rebbe Nachman made a promise no other Tzaddik in the whole of Jewish history has ever made. Taking two of his closest followers as witnesses, he said: `When my days are ended and I leave this world I will intercede for anyone who comes to my grave, recites the Ten Psalms of the Tikkun HaKlali, and gives some charity. No matter how serious his sins and transgressions, I will do everything in my power to save him and cleanse him. I will span the length and breadth of the Creation for him. By his peyot, his sidecurls, I will pull him out of Hell!' (Rabbi Nachman's Wisdom #141).
The practice of visiting the graves of the Tzaddikim to pray is an ancient one, going back to biblical times (Rashi, Numbers 13:22) and was well known in Talmudic times (see Sotah 13a; Zohar II:70b). Even today, many visit the cemetery before the High Holidays, to pray for good health and a successful year. After the death of the Tzaddik, his soul is permanently absorbed in God's infinity. Since according to the Kabbalah the nefesh, the lowest part of the soul, remains at the gravesite, this is a fitting place for Jews to pray to become attached to the infinity of God. While visiting the graves of Tzaddikim has its definite material benefits, the desire to be a good Jew, to serve God with all one's heart, is the focal point of the trip to Uman.