Wordpress - Link to user's profile settings page?

The user edit page of the current user is /wp-admin/profile.php, so you can just do admin_url( 'profile.php' ), which is the way it is used in the WP source code.

Combination of other answers:

<a href="<?php echo admin_url( 'user-edit.php?user_id=' . $curauth->ID, 'http' ); ?>">Edit Profile</a>

I'm using this on author.php, that's why I've already got the user ID on the page. That way an admin gets a link to edit that user's profile rather than their own.

Possibly something like this?

<?php get_currentuserinfo();

global $user_ID;
if (” != $user_ID) { ?>

<a href="/wp-admin/user-edit.php?user_id=<?php the_author_ID(); ?>">Edit
Profile</a>

<?php } ?>