Creating new dropdown lists with a button

Great question, here is a solution you can implement pretty easily given your existing code.

Instead of (part of your existing code):

// Create a new text input
var newText = document.createElement('input');
newText.type = "text"; 

//for testing
newText.value = counter++;

// Append new text input to the newDiv
newDiv.appendChild(newText);

Use:

// create dropdown element and one option element
var newDropdown = document.createElement('select'),
    newDropdownOption = document.createElement("option");

// assign 'value' and 'text' properties to the option element   
newDropdownOption.value = "value1";
newDropdownOption.text = "option 1";

// add the option to the dropdown DOM node
newDropdown.add(newDropdownOption);

// add dropdown to mainContainer
newDiv.appendChild(newDropdown);

Hope that helps!

EDIT: here's the full working code. you should be able to take it from here!

function addNew() {

            // Get the main Div in which all the other divs will be added
            var mainContainer = document.getElementById('mainContainer');

            // Create a new div for holding text and button input elements
            var newDiv = document.createElement('div');

            // Create a new text input
            var newDropdown = document.createElement('select');

            newDropdownOption = document.createElement("option");
            newDropdownOption.value = "value1";
            newDropdownOption.text = "option 1";

            newDropdown.add(newDropdownOption);

            // Create buttons for creating and removing inputs
            var newAddButton = document.createElement('input');
            newAddButton.type = "button";
            newAddButton.value = " + ";

            var newDelButton = document.createElement('input');
            newDelButton.type = "button";
            newDelButton.value = " - ";

            // Append new text input to the newDiv
            newDiv.appendChild(newDropdown);

            // Append new button inputs to the newDiv
            newDiv.appendChild(newAddButton);
            newDiv.appendChild(newDelButton);

            // Append newDiv input to the mainContainer div
            mainContainer.appendChild(newDiv);

            // Add a handler to button for deleting the newDiv from the mainContainer
            newAddButton.onclick = addNew;

            newDelButton.onclick = function() {
                    mainContainer.removeChild(newDiv);
            };
        }

Adding HTML: I've been going off of the HTML you provided, so this should work just fine.

<div id="mainContainer">
    <select name="text">
        <option value="t1">t1</option>
        <option value="t2">t2</option>
        <option value="t3">t3</option>
    </select>
    <input type="button" value=" + " onClick="addNew();">
</div>