function countNum(){
          //alert($('input[name=check]:checked').length);
         var arrays = new Array();
          var items = document.getElementsByName("check");
          for(var i=0;i<items.length;i++){
              if(items[i].checked){
                  arrays.push(items[i].value);
              }
          }
          alert(arrays.length);
        }

    <input type="checkbox" value="1" name="check" checked/>
    <input type="checkbox" value="2" name="check"/>
    <input type="checkbox" value="3" name="check"/>
    <input type="button" value="選中個數" id="btn" onclick="countNum();">