My interest was caught by an article talking about the mundane and supermundane powers which are mentioned in the Samaññaphala Sutta (The Fruits of the Contemplative Life, DN 2):
The first five mundane powers: (can be attained through perfection of samādhi)
- Supranormal powers
With his mind thus concentrated, purified, and bright, unblemished, free from defects, pliant, malleable, steady, and attained to imperturbability, he directs and inclines it to the modes of supranormal powers. He wields manifold supranormal powers. Having been one he becomes many; having been many he becomes one. He appears. He vanishes. He goes unimpeded through walls, ramparts, and mountains as if through space.
- Clairaudience
With his mind thus concentrated, purified, and bright, unblemished, free from defects, pliant, malleable, steady, and attained to imperturbability, he directs and inclines it to the divine ear-element. He hears -- by means of the divine ear-element, purified and surpassing the human -- both kinds of sounds: divine and human, whetever near or far.
- Mind Reading
With his mind thus concentrated, purified, and bright, unblemished, free from defects, pliant, malleable, steady, and attained to imperturbability, he directs and inclines it to knowledge of the awareness of other beings. He knows the awareness of other beings, other individuals, having encompassed it with his own awareness.
- Recollection of Past Lives
With his mind thus concentrated, purified, and bright, unblemished, free from defects, pliant, malleable, steady, and attained to imperturbability, he directs and inclines it to knowledge of the recollection of past lives. He recollects his manifold past lives, i.e., one birth, two births, three births, four, five, ten, twenty, thirty, forty, fifty, one hundred, one thousand, one hundred thousand, many aeons of cosmic contraction, many aeons of cosmic expansion, many aeons of cosmic contraction and expansion, [recollecting], 'There I had such a name, belonged to such a clan, had such an appearance.
- The Passing Away & Re-appearance of Beings
With his mind thus concentrated, purified, and bright, unblemished, free from defects, pliant, malleable, steady, and attained to imperturbability, he directs and inclines it to knowledge of the passing away and re-appearance of beings.
One supermundane power (Can be attained through Vipassana):
- The Ending of Mental Fermentations
With his mind thus concentrated, purified, and bright, unblemished, free from defects, pliant, malleable, steady, and attained to imperturbability, the monk directs and inclines it to the knowledge of the ending of the mental fermentations.
However, the Buddha emphasized to attain only the last through the realization of Arahatship. It might be unfair to ask for scientific proof, but is there any backup for the first five supposedly attainable powers, any personal experiences maybe?