user2265: Buddha and others repeatedly says that those that have genuine samadhi can easily cultivate the Six Paranormal Powers--if they have not experienced them by accident already. The Path of Purification even outlines the step-by-step method to cultivate them after obtaining concentration attainment.
In the Taoist tradition there are plenty of stories of such immortals and super-powered people, some of them even very modern, such as the Youtube video of John Chang emitting fire through his hands. [The books that are based on him are very awesome and interesting, like The Magus of Java.]
What are some modern accounts in the Buddhist tradition?
When I meet Buddhist people and others, they often say they have samadhi but they seem quite ordinary to me. Oftentimes, I am convinced that they make claims of samadhi merely to gain a following--however small it may be.

user8157: The Buddha forbade monks to demonstrate psychic powers to lay people. Therefore, at least in Theravada Buddhism, it is uncommon to meet Buddhists claiming & displaying psychic powers. 
The monks rules state:


Should any bhikkhu report (his own) superior human state to an unordained person, when it is factual, it is to be confessed.
  Displaying psychic powers. A related rule at Cv.V.8.2 states that to
  display psychic powers to lay people is a dukkata [offense]. 


Page 263 to 266


Psychic powers are said to occur only in individuals with a latent pre-disposition. For example, many arahants, such as Venerable Sariputta, a jhana master, did not have supernormal powers.
Therefore, the Buddha could not have repeatedly said that [all of] those that have genuine samadhi can easily cultivate the Six Paranormal Powers. In the Susima Sutta, it is reported the Buddha explains to Susima that development of psychic powers is not a prerequisite for enlightenment.
Therefore, suttas such as Kayagata-sati Sutta (quoted below) that generalise about samadhi & powers are probably fake. 

Monks, for one in whom mindfulness immersed in the body is
  cultivated, developed, pursued, handed the reins and taken as a basis,
  given a grounding, steadied, consolidated, & well-undertaken, ten
  benefits can be expected. Which ten?
[5] "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, & mountains as if through
  space. He dives in & out of the earth as if it were water. He walks on
  water without sinking as if it were dry land. Sitting crosslegged he
  flies through the air like a winged bird. With his hand he touches &
  strokes even the sun & moon, so mighty & powerful. He exercises
  influence with his body even as far as the Brahma worlds.
[6] "He hears — by means of the divine ear-element, purified &
  surpassing the human — both kinds of sounds: divine & human, whether
  near or far.
[7] "He knows the mind of other beings, other individuals, having
  encompassed it with his own mind....

The Buddha himself did not think highly of psychic powers (Kevatta Sutta) despite often using psychic powers to only help monks with their practise (example, Sona Sutta). 
We must also understand the Buddha's enemies, such as Devadatta & Mara, had psychic powers. 
In summary, psychic powers are 100% unrelated to the goal of Buddhism. 

2265: <p>Buddha and others repeatedly says that those that have genuine samadhi can easily cultivate the Six Paranormal Powers--if they have not experienced them by accident already. The Path of Purification even outlines the step-by-step method to cultivate them after obtaining concentration attainment.</p>

<p>In the Taoist tradition there are plenty of stories of such immortals and super-powered people, some of them even very modern, such as the <a href="http://blog.asiantown.net/-/9042/indonesian-man-burns-paper-with-the-electric-power-inside-his-body.aspx" rel="nofollow">Youtube video of John Chang emitting fire through his hands</a>. [The books that are based on him are very awesome and interesting, like The Magus of Java.]</p>

<p><strong>What are some modern accounts in the Buddhist tradition?</strong></p>

<p>When I meet Buddhist people and others, they often say they have samadhi but they seem quite ordinary to me. Oftentimes, I am convinced that they make claims of samadhi merely to gain a following--however small it may be.</p>
 8157: <p>The Buddha forbade monks to demonstrate psychic powers to lay people. Therefore, at least in Theravada Buddhism, it is uncommon to meet Buddhists claiming &amp; displaying psychic powers. </p>

<p>The monks rules state:</p>

<blockquote>
  <ol start="8">
  <li>Should any bhikkhu report (his own) superior human state to an unordained person, when it is factual, it is to be confessed.
  Displaying psychic powers. A related rule at Cv.V.8.2 states that to
  display psychic powers to lay people is a dukkata [offense]. </li>
  </ol>
  
  <blockquote>
    <p><a href="http://www.accesstoinsight.org/lib/authors/thanissaro/bmc1.pdf" rel="nofollow">Page 263 to 266</a></p>
  </blockquote>
</blockquote>

<p>Psychic powers are said to occur only in individuals with a latent pre-disposition. For example, many arahants, such as Venerable Sariputta, a jhana master, did not have supernormal powers.</p>

<p>Therefore, the Buddha could not have repeatedly said that [all of] those that have genuine samadhi can easily cultivate the Six Paranormal Powers. In the <a href="http://www.accesstoinsight.org/tipitaka/sn/sn12/sn12.070.than.html" rel="nofollow">Susima Sutta</a>, it is reported the Buddha explains to Susima that development of psychic powers is not a prerequisite for enlightenment.</p>

<p>Therefore, suttas such as <a href="http://www.accesstoinsight.org/tipitaka/mn/mn.119.than.html" rel="nofollow">Kayagata-sati Sutta</a> (quoted below) that generalise about samadhi &amp; powers are probably fake. </p>

<blockquote>
  <p>Monks, for one in whom mindfulness immersed in the body is
  cultivated, developed, pursued, handed the reins and taken as a basis,
  given a grounding, steadied, consolidated, &amp; well-undertaken, ten
  benefits can be expected. Which ten?</p>
  
  <p>[5] "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, &amp; mountains as if through
  space. He dives in &amp; out of the earth as if it were water. He walks on
  water without sinking as if it were dry land. Sitting crosslegged he
  flies through the air like a winged bird. With his hand he touches &amp;
  strokes even the sun &amp; moon, so mighty &amp; powerful. He exercises
  influence with his body even as far as the Brahma worlds.</p>
  
  <p>[6] "He hears — by means of the divine ear-element, purified &amp;
  surpassing the human — both kinds of sounds: divine &amp; human, whether
  near or far.</p>
  
  <p>[7] "He knows the mind of other beings, other individuals, having
  encompassed it with his own mind....</p>
</blockquote>

<p>The Buddha himself did not think highly of psychic powers (<a href="http://www.accesstoinsight.org/tipitaka/dn/dn.11.0.than.html" rel="nofollow">Kevatta Sutta</a>) despite often using psychic powers to only help monks with their practise (example, <a href="http://www.accesstoinsight.org/tipitaka/an/an06/an06.055.than.html" rel="nofollow">Sona Sutta</a>). </p>

<p>We must also understand the Buddha's enemies, such as Devadatta &amp; Mara, had psychic powers. </p>

<p>In summary, psychic powers are 100% unrelated to the goal of Buddhism. </p>
