Is it possible to remove/hide the “New” button?

We use homepage components which analyse the page, and use javascript to remove/add buttons where we have no other choice to do so. But this implies developing with a high dependency on the salesforce html output .. which is not guaranteed to stay unchanged, this is something to strongly consider if you would explore this approach.

Why do you want to remove the new button ? If there are groups of users who should not make opportunities, you may want to restrict them access through their profile.

update: For instance, using jquery:

if (document.location.href.toString().indexOf("/a49/o") != -1) {
$('input[name=new]').hide();
}

You would need to update the Id when migrating code between sandboxes/organisations