Non-attachment is a fundamental concept in virtually all contemplative traditions. You could even say that the only difference between a St. John of the Cross and the Buddha's presentation of the Four Noble Truths in the Pali Canon is that St. John commends non-attachment from all things so that one can be ultimately and completely attached to God.
Union with God and Nibbana could also, almost, be equated depending on how much similarity you want to see in the traditions.
You could also draw comparisons between the final stages of Jhana meditation, which, supposedly, Buddha was practicing on the day of his Enlightenment, with the Christian concept of contemplation. In the final stages of Jhana meditation, one is absorbed into "the base of boundless consciousness," "the base of nothingness," "the base of neither perception nor non-perception," while the Christian contemplative is "absorbed into God."
Although St. John of the Cross and Siddhartha Gautama come from different theoretical viewpoints, one could argue that they are experiencing virtually the same thing.
Of course this depends on how much similarity you want to emphasize between the traditions. But the parallels stand out to me.