10-15 items in a horizontal nav bar is really too many. Scanning a horizontal list is much more difficult and less natural compared to a vertical list. Also it's likely that only at very large window sizes will you avoid the problem you're having now — not enough space for all the items.
So, first vote is work on the IA.
Second, re: "how does a user know which page they're on and which option was selected?" In my view a highlighted nav bar item should be only a helpful add-on to knowing what page you are on. That is, a user should be able to clearly see where they are on your site without needing to see the nav. The easiest way to do this is with large and clear headers on each page.
Breadcrumbs, as you suggest, are another common way of dealing with location. I think it is reasonable to have breadcrumbs on only one section of your site if that section is indeed much more complex than the rest of your site.
The case of subpages hidden behind menus shows exactly why you shouldn't rely on the nav bar to indicate where a user is on your page.
Check out USA Today's Sports page and use their sport sub-nav. While they do highlight if you choose a sport in the main top row, they don't do anything special if you select a sport in the MORE dropdown. The big text at the top of each section does the work and the highlighting of the nav is nice if it's there, but not that big of a problem if it's not.
So if the site itself (not the nav) is doing the work of showing users where they are you don't need to worry about the current page's nav item being off the screen or behind a "more" link.
Third: If you do need to put 10-15 items in a horizontal nav bar and feel nav-bar highlighting IS too important to hide the highlighting behind a 'more' link, then I suggest 1. alphabetizing the list, and 2. cropping the nav bar as needed and allow the user to slide the nav bar left or right with a mouse hover on either end. This way can make the current page nav item visible and allow them to access the rest of the nav. Alphabetizing is important because it will reduce hunting when trying to find the link you're looking for.
I'm not sure I've seen this done before — it would need some real world testing to see if people would intuitively understand it.