Legen Sie Standardwerte ungleich Null für die Eingabevariable(n) fest.
$contact = new Contact;
$contact->name = Input::get('name');
$contact->username = Input::get('username', '');
$contact->save();
Oder, in neueren Laravel-Versionen:
$contact = new Contact;
$contact->name = $request->input('name');
$contact->username = $request->input('username', '');
$contact->save();