[FINoM]

<input type="checkbox" name="option1" value="a1" id="id1"> Удалить1<br>
<input type="checkbox" name="option2" value="a2" id="id2"> Удалить2<br>
<input type="checkbox" name="option3" value="a3" id="id3"> Удалить3<br> 
<input type="checkbox" name="option4" value="a4" id="id4"> Удалить4<br> 
<input type="checkbox" name="option5" value="a5" id="id5"> Удалить5
<input type="button" id="delete" value="DELETE">
<script>
document.getElementById('delete').addEventListener('click', function(){
   var inputs = document.getElementsByTagName('input'),
   array = [];
   for(var i = 0; i < inputs.length; i++) {
      if(inputs[i].type === 'checkbox' && inputs[i].checked) {
           array.push(inputs[i].id)
      }
   }

   alert(array);
});
</script>