Are there are any good modern replacement for this?
Breadcrumbs are used to aid the user in navigation. Whether to use them or not depends on how your information is structured and how large your site is (how deep it goes). Not on how "old" it is.
If your site hierarchy is simple and users can rely on the main navigation or the back button to quickly get to some place they want, you can leave the breadcrumbs out.
If it's not - and you want your users to be able to find things easily, consider re-looking at your information architecture and decide how changes to your IA or adding breadcrumbs can benefit the user.
This article on Smashing Magazine: Bread Crumbs in Web Design explains the best practices in using bread crumbs and when to avoid them.