For the WooCommerce plugin for WordPress, this function returns all variations of a product by referencing the product ID.

woocommmerce-product-variations.php

<?php /*
Takes a product ID and returns an array that includes all types of variations of the product, and the attributes of that variation. 
Variations are normally returned as a term object. They belong to the original product ID and the taxonomy name is equal to the attribute name.
If a custom variation is provided instead of a term object, the variation will simply be a string of the option's name.

Example return result is given below. This is a single product with one attribute and two different variations.

Array (
  [pa_oregon-training-classes] => Array (
      [attribute] => Array (
          [name] => pa_oregon-training-classes
          [value] => 
          [position] => 2
          [is_visible] => 1
          [is_variation] => 1
          [is_taxonomy] => 1
      ),

      [variations] => Array (
          [09252013-6-00pm-salem] => stdClass Object (
              [term_id] => 30
              [name] => 05/27/13 -6:00pm- Salem, OR
              [slug] => 05252013-6-00pm-salem
              [term_group] => 0
              [term_taxonomy_id] => 30
              [taxonomy] => pa_oregon-training-classes
              [description] => No materials required. Upon completion of class, student receives the certificate for the class
              [parent] => 0
              [count] => 2
            ),
            
          [09252013-6-00pm-salem] => stdClass Object (
              [term_id] => 30
              [name] => 05/27/13 -6:00pm- Salem, OR
              [slug] => 05252013-6-00pm-salem
              [term_group] => 0
              [term_taxonomy_id] => 30
              [taxonomy] => pa_oregon-training-classes
              [description] => No materials required. Upon completion of class, student receives the certificate for the class
              [parent] => 0
              [count] => 2
            ),
            
            ...
      )
) 

*/
function woo_get_product_variations( $product_id ) {
  $product_variations = array();

  // Make sure we are working with a product ID here
  if ( is_object($product_id) ) {
    if ( property_exists($product_id, 'id') ) $product_id = $product_id->id;
    else if ( property_exists($product_id, 'ID') ) $product_id = $product_id->ID;
  }
  if ( !$product_id || get_post_type( $product_id ) !== 'product' ) return false;
  
  // Get attributes of the base product. All variations are stored as an attribute in this custom post meta field. See: writepanel-product-type-variable.php
  $attributes = maybe_unserialize( get_post_meta( $product_id, '_product_attributes', true ) );
  
  // Loop through all attributes in search of variations
  foreach ( $attributes as $attribute ) {
  
    // Only deal with variations
    if ( ! $attribute['is_variation'] ) continue;

    // Prepare a new variations array which we will add our individual variations to
    if ( isset($attribute['name']) ) {
      $variation = &$product_variations[ $attribute['name'] ];
    }else{
      $variation = &$product_variations[];
    }
    
    $variation['attribute'] = $attribute;
    $variation['variations'] = array();

    // Get terms for attribute taxonomy or value if its a custom attribute
    if ( $attribute['is_taxonomy'] ) {
      
      // Variation is a taxonomy, add each term to the attribute
      $post_terms = wp_get_post_terms( $product_id, $attribute['name'] );
      
      foreach ( $post_terms as $term ) {
        $variation['variations'][ $term->slug ] = $term;
      }

    } else {

      // Variation is a custom attribute, separated by vertical pipes. Split the pipes and return them as a basic string.
      $options = array_map( 'trim', explode( '|', $attribute['value'] ) );

      foreach ( $options as $option ) {
        $variation['variations'][ sanitize_title( $option ) ] = $option;
      }

    }
  }
  
  return $product_variations;
}