Display tweets in WordPress using Twitter API v1.1 - With authentication and a fallback when Twitter is down. Full explanation here: http://www.problogdesign.com/wordpress/authenticate-your-twitter-api-calls-before-march/

WordPress-Tweet-List.php

<?php
/* REQUIRES: TwitterOAuth
 *    https://github.com/abraham/twitteroauth/tree/master/twitteroauth
 *
 *    Download and place in a /twitteroauth/ folder in your theme/plugin.
 *
 *
 * Full guide here: http://www.problogdesign.com/wordpress/authenticate-your-twitter-api-calls-before-march/
 * 
 * Uses:
 * Twitter API call:
 *     http://dev.twitter.com/doc/get/statuses/user_timeline
 * WP transient API.
 *		http://www.problogdesign.com/wordpress/use-the-transients-api-to-list-the-latest-commenter/
 */

$numTweets      = 3;                // Number of tweets to display.
$name           = 'problogdesign';  // Username to display tweets from.
$excludeReplies = true;             // Leave out @replies
$transName      = 'list-tweets';    // Name of value in database.
$cacheTime      = 5;                // Time in minutes between updates.

$backupName = $transName . '-backup';

// Do we already have saved tweet data? If not, lets get it.
if(false === ($tweets = get_transient($transName) ) ) :	

  // Get the tweets from Twitter.
  include 'twitteroauth/twitteroauth.php';
  
  $connection = new TwitterOAuth(
    'xxxxxxxxxxxxxxxxxxxxxx',   // Consumer key
    'xxxxxxxxxxxxxxxxxxxxxx',   // Consumer secret
    'xxxxxxxxxxxxxxxxxxxxxx',   // Access token
    'xxxxxxxxxxxxxxxxxxxxxx'    // Access token secret
  );
  
  // If excluding replies, we need to fetch more than requested as the
  // total is fetched first, and then replies removed.
  $totalToFetch = ($excludeReplies) ? max(50, $numTweets * 3) : $numTweets;
  
  $fetchedTweets = $connection->get(
    'statuses/user_timeline',
    array(
      'screen_name'     => $name,
      'count'           => $totalToFetch,
      'exclude_replies' => $excludeReplies
    )
  );
  
  // Did the fetch fail?
  if($connection->http_code != 200) :
    $tweets = get_option($backupName); // False if there has never been data saved.
    
  else :
    // Fetch succeeded.
    // Now update the array to store just what we need.
    // (Done here instead of PHP doing this for every page load)
    $limitToDisplay = min($numTweets, count($fetchedTweets));
    
    for($i = 0; $i < $limitToDisplay; $i++) :
      $tweet = $fetchedTweets[$i];
    
      // Core info.
      $name = $tweet->user->name;
      $permalink = 'http://twitter.com/'. $name .'/status/'. $tweet->id_str;

      /* Alternative image sizes method: http://dev.twitter.com/doc/get/users/profile_image/:screen_name */
      $image = $tweet->user->profile_image_url;

      // Message. Convert links to real links.
      $pattern = '/http:(\S)+/';
      $replace = '<a href="${0}" target="_blank" rel="nofollow">${0}</a>';
      $text = preg_replace($pattern, $replace, $tweet->text);

      // Need to get time in Unix format.
      $time = $tweet->created_at;
      $time = date_parse($time);
      $uTime = mktime($time['hour'], $time['minute'], $time['second'], $time['month'], $time['day'], $time['year']);

      // Now make the new array.
      $tweets[] = array(
              'text' => $text,
              'name' => $name,
              'permalink' => $permalink,
              'image' => $image,
              'time' => $uTime
              );
    endfor;

    // Save our new transient, and update the backup.
    set_transient($transName, $tweets, 60 * $cacheTime);
    update_option($backupName, $tweets);
  endif;
endif; 

// Now display the tweets.
?>
<ul id="tweets">  
  <?php foreach($tweets as $t) : ?>
    <li>
      <p>
        <?php echo $t['text']; ?>
        <span class="tweet-time"><?php echo human_time_diff($t['time'], current_time('timestamp')); ?> ago</span>
      </p>
    </li>
  <?php endforeach; ?>
</ul>

1. $transName needs to be unique otherwise forget about multiple tweets on the same page!
2. if(false === ($tweets = get_transient($transName) ) ) is not necessary. For some reason it evaluates TRUE more often than FALSE which results in blank twitts - regardless cache time.