This will be in your header.php, something like:
<title><?php bloginfo('name'); ?> | <?php wp_title(); ?></title>
Just change the vertical line to be included in the conditional, so that it shows on the other pages but not on the homepage, such as:
<title><?php bloginfo('name'); ?> <?php if ( is_single() ) { ?>| <?php } ?> <?php wp_title(); ?></title>
Or customise it any way you like, such as page title only:
<title><?php wp_title(); ?></title>