Thanks for the code. I ended up needing to be able to call each vocabulary individually since I didn't want to list all of my vocabularies on each node. To do this, I came up with the following code:

For template.php

<?php 
function mythemename_taxonomy_links($node, $vid) {

//if the current node has taxonomy terms, get them
  if (count($node->taxonomy)):

    $tags = array();
     foreach ($node->taxonomy as $term) {
	   if ($term->vid == $vid):
          $tags[] = l($term->name, taxonomy_term_path($term));
  		endif;
}
	if ($tags):
//get the vocabulary name and name it $name
    	$vocab = taxonomy_get_vocabulary($vid);
	    $name = $vocab->name;
        $output .= t("$name") . ": " . implode(' | ', $tags);
    endif;

  endif;

 	if ($output):
       return $output;
 	endif;

}
?>

For node.tpl.php

Note: 1 is the vid for the vocabulary I want to call.

<?php print mythemename_taxonomy_links($node, 1); ?>

Please let me know if you see a better way to do this.

In all of the examples above, if you want the Taxonomy Image shown instead, change the l($term->name, taxonomy_term_path($term)) to taxonomy_image_display($term->tid).

NancyDru

Here is what I use in D6 to return a themed list of terms by vocabulary ID:

function yourthemename_taxonomy_links($node, $vid) {
  if (count($node->taxonomy)){
    $tags = array();
    foreach ($node->taxonomy as $term) {
       if ($term->vid == $vid){
          $tags[] = array('title' => $term->name, 'href' => taxonomy_term_path($term), 'attributes' => array('rel' => 'tag'));
       }
		}
    if ($tags){
      return theme_links($tags, array('class'=>'links inline'));
    }
  }
}

To make this work in Drupal 6 (printing out all terms for each node preceded by vocabulary headings for all vocabularies), just change the function line to:

function yourthemename_print_terms($node)

and change the following line to use $node rather than $nide:

         $terms = taxonomy_node_get_terms_by_vocabulary($node, $vocabulary->vid);

Then in the node.tpl.php file, replace "print $terms" with:

print yourthemename_print_terms($node)

(remember to always replace "yourthemename" with your theme name in all files.)

The completed code for use in D6 is:

<?php
// split out taxonomy terms by vocabulary
function yourthemename_print_terms($node) {
     $vocabularies = taxonomy_get_vocabularies();
     $output = '<ul>';
     foreach($vocabularies as $vocabulary) {
       if ($vocabularies) {
         $terms = taxonomy_node_get_terms_by_vocabulary($node, $vocabulary->vid);
         if ($terms) {
           $links = array();
           $output .= '<li>' . $vocabulary->name . ': ';
           foreach ($terms as $term) {
             $links[] = l($term->name, taxonomy_term_path($term), array('rel' => 'tag', 'title' => strip_tags($term->description)));
           }
           $output .= implode(', ', $links);
           $output .= '</li>';
         }
       }
     }
     $output .= '</ul>';
     return $output;
}
?>

Is it just me or does this not work for translated taxonomy terms? I have a vocabulary whose term names are translated into different languages. But with this function, only the original name is displayed. I tried both the Handbook versions and NancyDru's.

edit: Okay, this works for term and vocab string translation if your taxonomy translation option is "Localize terms. Terms are common for all languages, but their name and description may be localized." Specify each the $vid in the node.tpl.php when you call the function.
Code borrowed from i18n_taxonomy. I am not 100% sure if this is the right way to do it, so caution is advised. You can copy the lines to the code in the handbook page as well.

// Split out taxonomy terms by vocabulary.
function yourthemename_print_terms($node, $vid) {
  $vocabularies = taxonomy_get_vocabularies();
  $vocs = array();
   foreach($vocabularies as $vocabulary) {
    $terms = taxonomy_node_get_terms_by_vocabulary($node, $vocabulary->vid);
        // Get the translated strings for the term names
	$terms = i18ntaxonomy_localize_terms($terms, $fields = array('name'));
    if ($terms) {
      $links = array();
      foreach ($terms as $term) {
        $links[] = l($term->name, taxonomy_term_path($term),
          array('attributes' => array('rel' => 'tag', 'title' => strip_tags($term->description))));
      }
      // Get the translated string for the vocab name	 
      $vname = i18nstrings("taxonomy:vocabulary:$vid:name", $vocabulary->name);
      // The 'children' element gives us a nested list.
      $vocs[] = array('data' => check_plain($vocabulary->name) . ': ', 'children' => $links);
    }
  }
  return theme('item_list', $vocs);
}

I wanted a bit more control in theming, without having to write too much more CSS than I already have. So here is my (6.x) version.

<?php
function yourtheme_print_terms($node, $inline = FALSE){
	$vocabularies = taxonomy_get_vocabularies();
	$output = '<div class="terms' . ($inline ? ' terms-inline': '') . '">';
	$inline_class = $inline ? ' inline' : '';
	foreach($vocabularies as $vocabulary){
		if($terms = taxonomy_node_get_terms_by_vocabulary($node, $vocabulary->vid)){
			$vocab = strtolower(str_replace(' ', '_', str_replace('.', '',$vocabulary->name)));
			$output .= '<ul class="links' . $inline_class . ' vocabulary ' . $vocab . '-terms">';
			foreach ($terms as $term){
				$output .= '<li class="term ' . $vocab . '-term ' . 'term-'. strtolower(str_replace(' ', "_", str_replace('.', '',$term->name))) . '">';
				$output .= l($term->name, taxonomy_term_path($term), array('rel' => 'tag', 'title' => strip_tags($term->description)));
				$output .= '</li>';
			}
			$output .= '</ul>';
		}
	}
	$output .= '</div>';
	return $output;
}?>

This function takes an optional second argument, any ==TRUE value will add tags for inline list theming.
I changed the original spans to ul's, with the same structure as the default returned by print $terms, except that different vocabularies are split into sibling ul's.
I also added "vocabulary" and "term" classes, as well as [vocabulary]-terms and [vocabulary]-term, and term-[term] classes as appropriate to ul's and li's - after replacing spaces with underscores, removing periods, and lowercase-ing the vocabulary and term.

I've checked out previous comments. But had to remix code to my taste. Here are some features:

• Suggested in http://drupal.org/node/133223#comment-3245288 was my starting point, but output would rewrite core taxonomy classes. I think it's a bad idea as your user may just rename taxonomy term and you'll have to change the css for this term (if it was styled). My version sticks to standard drupal 'taxonomy_term_00' tid based approach.
• Some other variations would also miss nice core ul.links.inline trend. But with .links.inline you don't even need to style your new taxonomy output any special. It's already in core CSS

Here we go, this code goes to your template.php:

<?php
function YOURTHEME_print_terms($node){
	$vocabularies = taxonomy_get_vocabularies();
	foreach($vocabularies as $vocabulary){
		if($terms = taxonomy_node_get_terms_by_vocabulary($node, $vocabulary->vid)){
			$output .= '<div>';
			$output .= '<span>'. $vocabulary->name . ': </span>';
			$output .= '<ul class="links inline">';
			foreach ($terms as $term){
				$output .= '<li class="taxonomy_term_' . $term->tid . '">';
				$output .= l($term->name, taxonomy_term_path($term), array('rel' => 'tag', 'title' => strip_tags($term->description)));
				$output .= '</li>';
			}
			$output .= '</ul>';
			$output .= '</div>';
		}
	}
	return $output;
}
?>

I wanted a bit more class + reusable code for subthemes. So I've added this bit of preprocess to template.php:

<?php
function YOURTHEME_preprocess_node(&$vars, $hook) {
	//split terms by vocabulary
	$vars['terms_split'] = YOURTHEME_print_terms($vars['node']);
}
?>

Now to get your terms split by vocabularies just add to your node.tpl.php:
<?php print $terms_split; ?>

Or if you still want to print stacked terms, it is still there:

<?php print $terms; ?>

Have fun!

custom drupal themes

Thanks.

Slightly modified to use theme_item_list as the output

function print_terms($node) {
    $vocabularies = taxonomy_get_vocabularies();
    foreach($vocabularies as $vocabulary){
        if($terms = taxonomy_node_get_terms_by_vocabulary($node, $vocabulary->vid)){
            $title = $vocabulary->name;
           unset($links);
            foreach ($terms as $term){
              $links[] = l($term->name, taxonomy_term_path($term), array('rel' => 'tag', 'title' => strip_tags($term->description)));
            }
	$output .= theme('item_list', $links, $title);
        }
    	
   }
    return $output;
}

try this module
http://drupal.org/project/term_display
probably does most of what has been discussed above

Trying to get the vocabulary name with
$vocab = taxonomy_get_vocabulary($vid);
freezes the page render and causes the page to cut off. I ended up adding the following code instead so i could manually set my vocabulary name:

function templatename_taxonomy_links($node, $vid, $nameofvoc="") {

//if the current node has taxonomy terms, get them
  if (count($node->taxonomy)) {

    $tags = array();
    foreach ($node->taxonomy as $term) {
       if ($term->vid == $vid):
          $tags[] = l($term->name, taxonomy_term_path($term), array('rel' => 'tag', 'title' => strip_tags($term->description)));
          endif;
	}
    if ($tags) {
//get the vocabulary name and name it $name
		if ($nameofvoc=="") {
			$vocab = taxonomy_get_vocabulary($vid);
			$name = $vocab->name;
		} else {
			$name = $nameofvoc;
		}
        $output = "<div class=\"section\">".t("$name") . ":</strong><br />" . implode(' | ', $tags)."</div>";
       return $output;
    }

 } else {
   return;
 }

}

Here's what you put in the node template:
<?php print templatename_taxonomy_links($node, 1, "vocabulary name goes here"); ?>
It is a temporary fix, I know. I want to actually fix the problem and not have to resort to this work-around.

To hide certain taxonomy vocabularies from a node is D6 GiorgosK's suggested module worked well for me: http://drupal.org/project/term_display

There isn't really any documentation for it, but basically you go to /admin/content/taxonomy/ and edit the vocabulary you wish to hide and in the display options choose display style: none.