An "Add" button that clones an item, and a "Remove" button that fades and removes an item I was looking into removing multiple inputs and selects at once using jQuery, but I couldn't find a solution, so I ended up with the following code:

$(function() {

  $('a.add').click(function(evt) {
    //clone lists
    //is there any way to simplify this part --begin--
    $('#s0 option').clone().appendTo('#s'+obj);
    $('#i0 option').clone().appendTo('#i'+obj);
    $('#r0 option').clone().appendTo('#r'+obj);
    $('#ieu0 option').clone().appendTo('#ieu'+obj);
    $('#ied0 option').clone().appendTo('#ied'+obj);
    //--end--
    evt.preventDefault(); //prevents scrolling
  });

  //remove inputs/selects
  $('a.remove').click(function(evt) {
    //animation is not necessary. How can I simplify this code? --begin--
    $('#comp'+x).animate({opacity:"hide"}, "slow").remove();
    $('#ppt'+x).animate({opacity:"hide"}, "slow").remove();
    $('#ct'+x).animate({opacity:"hide"}, "slow").remove();
    $('#p'+x).animate({opacity:"hide"}, "slow").remove();
    $('#ipvs'+x).animate({opacity:"hide"}, "slow").remove();
    $('#s'+x).remove();
    $('#i'+x).remove();
    $('#r'+x).remove();
    $('#ipvs'+x).remove();
    $('#other'+x).remove();
    //--end--
  } 
  evt.preventDefault();
  });
});


How can the sections marked between --begin-- and --end-- be simplified/improved?
I would go with ChrisThompson's method of adding classes and referring to them. 
But to answer your question straight and simple 

the first block can look like 

$.each( ['s','i','r','ieu','ied'], function(index,item){
        $('#' + item + '0 option').clone().appendTo('#' + item + obj );
    });


However, you did not specify what obj is

The second block can use the same technic to be simplified. 

The entire code would look something like this

$(function() {
  $('a.add').click(function(evt) {
    //clone lists
    //is there any way to simplify this part --begin--
    $.each( ['s','i','r','ieu','ied'], function(index,item){
        $('#' + item + '0 option').clons().appendTo('#' + item + obj );
    });
    //--end--
    evt.preventDefault(); //prevents scrolling
  });

  //remove inputs/selects
  $('a.remove').click(function(evt) {
    //animation is not necessary. How can I simplify this code? --begin--
    $.each( ['comp','ppt','ct','p','ipvs'], function(index,item){ $('#' + item + x).animate({opacity:"hide"} ,"slow").remove();});
    $.each(['s','i','r','other'], function(index,item){ $('#'+item+x).remove()});
    //--end--
    evt.preventDefault();
  } 
  });
});


However, it seems to me you are using too complex HTML structure. 
you need to 


Stop using IDs, and start using classes for elements that have things in common
For example : 


Instead of cloning each item, you can wrap all of the in a DIV and simple use html() to clone the entire HTML. When you inject the HTML to some other div, give the new wrapper div an ID. 


For example 

$(".my-form").append($("&lt;div/&gt;").addClass(".object-item").attr("id","newObject" + $(".my-form .object-item").length ).html( $(".items-to-clone-wrapper").html() );


You then have a unique identifier for every element on the page. for example $("#newObject1 .s") instead of $("#s1"). 

Here is a fiddle I made on the assumptions I made about your code. I hope it will be of use to you. please let me know if there's something I can do.