So many people trying to enable and you want to disable... 

<1>

Central Administration > Application Management > Authentication Providers > Edit Authentication

Put "Enable Client Integration?" as No.

Client Integration:Disabling client integration will remove features which launch client applications. Some authentication mechanisms (such as Forms) don't work well with client applications. In this configuration, users will have to work on documents locally and upload their changes.  

With this you will disable activeX options and others like connect to outlook and connecto to Access. 

<2>

Open sharepoint designer, open you sharepoint site, open you list or document library, open upload.aspx file and hide code that call multiple upload link.

Edit the file upload page in FrontPage.
Switch to Code view.
Modify the function EnsureUploadCtl to return 0;.

function EnsureUploadCtl()
{
 return 0;
}

<3>

The quickest way to hide multiple upload option from users for ALL document library is through css. 

C:\Program Files\Common Files\Microsoft Shared\web server extensions\12\TEMPLATE\LAYOUTS\1033\STYLES/Core.css

Add #ctl00_PlaceHolderMain_ctl01_ctl02_UploadMultipleLink { display: none } to your custom css will hide the Multiple Upload link.

I am not too sure about the scenario that you may need. But just for a fun purpose i though if we have multiple file upload menu then what to do with single file upload menu, anyways you can upload the single file with multiple file upload menu.

I though let me hide that manu just for a fun purpose.

(1) Add content editor webpart on AllItems.aspx of your document library.
(3) Open Source editor
(4) Paste the following lines of code and see, your single upload will get disabled

<script type="text/javascript">
function GetElementByText(tagName, title)
{
var a = document.getElementsByTagName(tagName);

for (var i=0; i < a.length; i++)
{
if (a[i].text)
{
if (a[i].text === title)
{
return a[i];
}
}
}

return null;
}

if (window.onload)
{
var oLoad = window.onload;
window.onload = function bodyLoad()
{
oLoad();

var o = GetElementByText("ie:menuitem","Upload Document");
if (o)
{
o.disabled = true;
}
}
}
</script>

That's it. Your job is done.

<5>

The 'Toolbar Manager' feature on CodePlex<http://www.codeplex.com/features> might be worth a look as well: Toolbar Manager This Feature allows you to selectively show and hide menu items on the standard list/library toolbar. The feature adds a new web part to the gallery that you can place on any list/library view page. Once placed on the page, you can use the properties of the web part to show or hide menu items. This is the perfect solution for hiding a single menu item such as "Export to Spreadsheet" to prevent users from taking that action.