Sure. You have to take an API key from a tile service.
var map = L.map('map').setView([36.7667, 13.5833], 13);
L.tileLayer('http://{s}.tile.cloudmade.com/74b831354f3554faa108ac65e3/997/256/{z}/{x}/{y}.png', {
attribution: 'Map data © <a href="http://openstreetmap.org">OpenStreetMap</a> contributors, <a href="http://creativecommons.org/licenses/by-sa/2.0/">CC-BY-SA</a>, Imagery © <a href="http://cloudmade.com">CloudMade</a>',
maxZoom: 18
}).addTo(map);
var marker = L.marker([36.752866, 13.556323]).addTo(map);
Please notice 74b831354f3554faa108ac65e3
. It's not going to work for you.
You can use this service to get a API KEY
EDIT 27 APR 2014: CloudMade is not free anymore. You can use: MapQuest, MapSurfer.NET or openstreetmap.de