Here is a quick script. I wrote for a co-worker.

var host = "localhost"
var port = 27000
var dbslist = db.adminCommand('listDatabases');

for( var d = 0; d < dbslist.databases.length; d++) {
     var db = connect(host+":"+port+"/"+dbslist.databases[d].name);
     var collections = db.getCollectionNames();
     for(var i = 0; i < collections.length; i++){
         var name = collections[i];
         if(name.substr(0, 6) != 'system') {
            print("\t"+dbslist.databases[d].name+"."+name + ' = ' + db[name].count() + ' records');
         }
     }
}