I'll start with the one that worked reliably for my website:

$current_url = home_url($_SERVER);

Now some will complain about using the "REQUEST_URI" option, so here some alternatives that proved to be not always reliable, depending on your circumstances.

// Option 1
// requires $wp, may not work with permalinks set to plain
global $wp; 
$current_url = home_url( $wp->request );

// Option 2
// requires $wp, may not work with permalinks set to plain
global $wp;
$current_url = add_query_arg( $wp->query_vars, home_url( $wp->request ) );

// Some other options that may be helpful:
$current_url = get_permalink( get_the_ID() ); // for page
$current_url = get_category_link( get_query_var( 'cat' ) ); // for category