How to remove Gravatar from Username column

This is an old thread, but just in case someone else needs it: starting in version 4.2, you can use the pre_get_avatar filter to bypass pulling the actual avatar and just sending back an empty string.

add_filter( 'pre_get_avatar', 'rkv_remove_avatar_from_list', 10, 3 );
/**
 * Remove the avatar from just the user list.
 *
 * @param string $avatar       HTML for the user's avatar. Default null.
 * @param mixed  $id_or_email  The Gravatar to retrieve. Accepts a user_id, gravatar md5 hash,
 *                             user email, WP_User object, WP_Post object, or WP_Comment object.
 * @param array  $args         Arguments passed to get_avatar_url(), after processing.
 *
 * @return string              An empty string.
 */
function rkv_remove_avatar_from_list( $avatar, $id_or_email, $args ) {

    // Do our normal thing on non-admin or our screen function is missing.
    if ( ! is_admin() || ! function_exists( 'get_current_screen' ) ) {
        return $avatar;
    }

    // Get my current screen.
    $screen = get_current_screen();

    // Bail without the object.
    if ( empty( $screen ) || ! is_object( $screen ) || empty( $screen->base ) || 'users' !== $screen->base ) {
        return $avatar;
    }

    // Return an empty string.
    return '';
}

There seems to be a filter for the get_avatar function. So I just output an empty string to it.

function remove_avatar_from_users_list( $avatar ) {
    if (is_admin()) {
        global $current_screen; 
        if ( $current_screen->base == 'users' ) {
            $avatar = '';
        }
    }
    return $avatar;
}
add_filter( 'get_avatar', 'remove_avatar_from_users_list' );

UPDATE: Restrict to 'All Users' page only.

1. You have to filter pre_option_show_avatars and return something that evaluates to FALSE but isn't FALSE. Let's say a 0.
2. You should restrict that filter to user list pages.
   • In a single-site the proper action is restrict_manage_users.
   • In a network management screen that could be restrict_manage_users-network, but that doesn't work, so we use the filter wpmu_users_columns and return whatever we get here.

Result:

add_filter( 'wpmu_users_columns', 'no_avatars_in_user_list' );
add_action( 'restrict_manage_users', 'no_avatars_in_user_list' );

function no_avatars_in_user_list( $in = NULL )
{
    add_filter( 'pre_option_show_avatars', '__return_zero' );
    return $in;
}

Since there is no special avatar column to unset (the avatars are inside the username column), you could try instead to hide the avatars via css:

function hide_avatars_wpse_94126() {
    if(!current_user_can('manage_options')){
        // hide only for non-admins
        echo "<style>.users td.username img.avatar{display:none !important;}</style>";
    }
}
add_action('admin_head-users.php','hide_avatars_wpse_94126');

where they are hidden for non-admins.

The result will be like this: