How do I display a field that's set to "Hidden" by the content type in the template? I have an existing site where a bunch of the fields are set to Hidden in the Display fields for the content type. I don't want to change that because I'm not 100% sure how that will affect other aspects of displaying the page.

When I do a var_export($node, TRUE) I can see the field values are present in the node, they just aren't being rendered in $content.

Can I use hook_nodeapi() to change the field display to "Default" or "Trimmed", etc?
$node->content will be a string containing the generated HTML output of the node's fields that will be displayed.

In hook_nodeapi() the $node->content is already generated, but you can append the hidden field's value to it if needed, with something like this:

function mymodule_nodeapi(&amp;$node, $op, $a3 = NULL, $a4 = NULL) {
    switch($op) {
        case 'view':
            if($node-&gt;type == "mytype") {
                $node-&gt;content .= "&lt;div&gt;".$node-&gt;field_myfield[0]['value']."&lt;/div&gt;";
            }
        break;
    }
}