I've looked and looked and attempted to locate a solution for which I have been searching for, however i haven't yet see a solution with this:

I'm trying to develop a Wordpress loop that can take all of the posts from one category and shows them three at any given time inside <li></li> tags.

Output need to look such as this:

<li>My post title | Another Title | Third title</li>
<li>The next post title | A different post | Post #6</li>
<li>And so on | And so forth</li>

I want this to loop through all of the records within the category until finished, after which exit the loop.

My code is totally non-working at this time, but I have provided what I am dealing with below. If anybody has any means to fix this, I'd like to give mad props for you, because this has hounded me for 3 days with no solution to date.

<?php // Loop through posts three at a time
$recoffsetinit = '0';
$recoffset = '3';
query_posts('cat=1&showposts=0');
$post = get_posts('category=1&numberposts=3&offset='.$recoffsetinit.');
while (have_posts()) : the_post(); 
?>
<li>
<?php
$postslist = get_posts('cat=1&order=ASC&orderby=title');
foreach ($postslist as $post) : setup_postdata($post);
 static $count = 0; if ($count == "3") { break; } else { ?>
 <a href="<?php the_permalink() ?>"></a>
<?php $count++; } ?>
<?php endforeach; ?>
<?php $recoffsetinit = $recoffset + $recoffsetinit; ?>
</li>
<?php endwhile; ?>

I compromised your solution to really make it work. It required just a little doing, since my code-fu isn't what you'd call "good." Here's the answer:

<ul>
<?php
query_posts('category=1&showposts=0');
$posts = get_posts('category_name=my_cat&order=ASC&orderby=title&numberposts=0'); 
$postsPerLine = 3;
$currentPostNumber = 0;

foreach ($posts as $post) :

    if ($currentPostNumber == 0) {
            echo '<li>';
    }
			?>

    <a href="<?php the_permalink(); ?>"></a>

    <?php
$currentPostNumber++;

    if ($currentPostNumber >= $postsPerLine) { 
            $currentPostNumber = 0;
            echo '</li>';
    }

  endforeach;
  ?>
</ul>

Just input!

No wordpress to check with, with no time, but something similar to this can be an easy method of carrying out it?

<?php

$postList = get_posts('cat=1&order=ASC&orderby=title');
$postsPerLine = 3;

echo "<ul>";
echo buildPosts($postList, $postsPerLine);
echo "</ul>";

function buildPosts($list, $perLine) {

    $out = '';
    $currentPostNumber = 0;

    foreach ($list as $post) {

    	if ($currentPostNumber == 0) {
    		$out .= '<li>';
    	}

    	$out .= "<a href='" . the_permalink() . "'></a> ";

    	$currentPostNumber++;

    	if ($currentPostNumber <= $perLine) { 
    		$currentPostNumber = 0;
    		$out .= '</li>';
    	}

    }
    return $out;
}

?>

Just snag all of the posts for any category, at the same time, then iterate regarding this. Produce a connect to every publish, add in the separator, as well as on every third publish begin a new <li>

<ul>
<?php
global $post;
$postsPerLine = 3;
$counter = 0;
$myposts = get_posts('category=1&orderby=title&order=ASC');

foreach($myposts as $post) :
    echo (++$counter % postsPerLine) ? : '<li>';
?>
    <a href="<?php the_permalink(); ?>"><?php the_title(); ?></a></li>
<?php
    echo ($counter % postsPerLine) ? ' | ' : '</li>';
endforeach;

?>
</ul>