Yes, I believe reincarnation is a fact and is part of God's plan for souls that have fallen into the Material Universe(s). Anyone who has 'remembered' a past life will know this. It is no coincidence that the greatest esoteric traditions of east and west, like the Jewish Kabbalah and the Vedic Tradition speak of the reality of reincarnation.
Reincarnation is actually a very deep topic, that deals with karma, psychic impressions/desires left on the subtle mind, and the reason souls have incarnated into the material universe, to begin with. If you read the Parable of the Prodigal Son you will understand man's predicament.
The Ultimate Goal as stated in the Bhagavad Gita (and other scriptures) is to end this cycle of death and rebirth and return to the pure spiritual world (which lies beyond the physical and astral afterlife realms). However, this desire only comes after many births and deaths, and will not be seen in what the gnostics called 'hylic' humanity. Those enchanted with the temporary pleasures of this world, those Prodigals who have just wandered into the far country, will not seek to return to the Father's House in this lifetime. Yet this does not mean they are eternally damned! What it means is they do not meet the qualification to enter the pure spiritual world, because they are still within the snare of material desires, and thus, must still go around on the Wheel of Samsara. Revelation 3:12 addresses this, as the first poster quoted.
The soul is wandering thru the Physical and Astral worlds, because of God-given Free Will and its need to explore duality and (perceived) separation from God. As one becomes more and more disillusioned with Maya and temporary pleasures, then they will seek the Supreme Reality, the realm of Sat-Chit-Ananda (Truth, Consciousness and Bliss). This desire is the foundation of all yoga practices and genuine spiritual seeking.