Removing the href
attribute definitely seems to the way to go. If for some reason you need it later, I would just store it in another attribute, e.g.
$(".my-link").each(function() {
$(this).attr("data-oldhref", $(this).attr("href"));
$(this).removeAttr("href");
});
This is the only way to do it that will make the link appear disabled as well without writing custom CSS. Just binding a click handler to false will make the link appear like a normal link, but nothing will happen when clicking on it, which may be confusing to users. If you are going to go the click handler route, I would at least also .addClass("link-disabled")
and write some CSS that makes links with that class appear like normal text.