Search for tags

Is it possible, to search just for tags?

Not any other taxonomies or post types, just tag titles.

Yes its very possible, you just need to create your own search form and processing function
form:

<form name="tag-search" method="POST" action="">
  <input type="text" vlaue="" name="tag-q" id="tag-q">
  <input type="submit" name="tag-submit" id="tag-submit" value="Search Tags">
</form>

processing:

<?php
if (isset($_POST['tag-submit']) && $_POST['tag-submit'] == "Search Tags" && isset($_POST['tag-q']) && $_POST['tag-q'] != ""){

    // @todo Sanity check and cleanup $_POST['tag-q'] here.

    $args = array('name__like' => $_POST['tag-q']);
    $tags = get_tags($args);
    $html="<div class="post_tags_search_r">";
    foreach ($tags as $tag){
        $tag_link = get_tag_link($tag->term_id);

        $html .= "<a href="https://wordpress.stackexchange.com/questions/13278/{$tag_link}" title="{$tag->name} Tag" class="{$tag->slug}">";
        $html .= "{$tag->name}</a>";
    }
    $html .= '</div>';
    echo $html;
}
?>

No this is something i have used in the past, the only downside to this is that name__like is case-insensitive so you might want to add the strtolower version to the name__like.