These two functions allow you two retrieve the products purchased by a user. One returns an array of all objects with crucial purchase log/cart info, the other returns true or false whether the specific product has been purchased.

wpsc-get-owned-products.php

<?php

function wpsc_get_owned_products( $user_id = false ) {
  global $user_purchases, $wpdb;
  
  // Get current user by default
  if ( !$user_id ) {
    $current = wp_get_current_user();
    if ($current) $user_id = $current->ID;
    else return false;
  }
  
  $user_id = intval($user_id);
  
  // Store user purchases in a global variable to prevent repeat SQL queries
  // Note that this is not desired if you need to check purchases before and after a checkout on a single page request!
  if ( !isset($user_purchases) ) $user_purchases = array();
  if ( !isset($user_purchases[$user_id]) ) {
  
    // SQL request for all of the user's purchases which are "owned" (Processed 3 or 5 -- Accepted Payment or Closed Order)
  	/*
    $sql = "
    SELECT * 
    FROM `" . WPSC_TABLE_PURCHASE_LOGS . "` 
    WHERE 
      `user_ID` IN ('" . $user_id . "')
      AND
      `processed` IN (3, 5)
    ORDER BY `date` DESC
    LIMIT 200";
    */
    
    $sql = "
    SELECT 
      `logs`.id as 'log_id',
      `logs`.user_ID as 'user_id',
      `cart`.id as 'cart_id',
      `cart`.prodid as 'product_id',
      `logs`.sessionid as 'sessionid',
      `logs`.processed as 'processed',
      `logs`.`date` as 'date'

    FROM `". WPSC_TABLE_PURCHASE_LOGS ."` AS `logs`
    INNER JOIN `". WPSC_TABLE_CART_CONTENTS ."` AS `cart`
      ON `logs`.id = `cart`.purchaseid

    WHERE
      `user_ID` IN (" . $user_id . ")
      AND
      `processed` IN (3, 5)

    GROUP BY `cart`.prodid
      
    ORDER BY `date` DESC

    LIMIT 200;";
    
		$user_purchases[$user_id] = $wpdb->get_results( $sql, ARRAY_A );
  }
  
  /* Return Value:
  Array (
    [0] => Array(
      [log_id] => 2
      [user_id] => 4
      [cart_id] => 2
      [product_id] => 452
      [sessionid] => 6131373064765
      [processed] => 3
      [date] => 1373064765
    ),
    ...
  )
  */
  
  return $user_purchases[$user_id];
}

function wpsc_user_owns_product( $product_id, $user_id = false ) {
  global $wpdb;
  
  // Get current user by default
  if ( !$user_id ) {
    $current = wp_get_current_user();
    if ($current) $user_id = $current->ID;
    else return false;
  }
  
  // Only look for post types: WPSC product
  if ( get_post_type( $product_id, 'wpsc-product' ) ) {
    $all_owned_products = wpsc_get_owned_products( $user_id );
    
    foreach( $all_owned_products as $purchase_log_item ) {
      if ($purchase_log_item['product_id'] == $product_id)
        return true;
    }
  }
 
  return false;
}