Here is a multitude of examples for the kind of music I'm looking for::

YouTube - Final Fantasy IX OST - Stirring the Forest ~ Evil Forest Theme (http://www.youtube.com/watch?v=uhrarEPCvqE)
YouTube - Brian Eno - Lantern Marsh (http://www.youtube.com/watch?v=xltFYEex-y4)
YouTube - Maple Story Music - Sleepywood (http://www.youtube.com/watch?v=-mve_E5l-kY)
YouTube - Mononoke - Kodamas (http://www.youtube.com/watch?v=sO6iESQUMew)

Though many of these are simple video game themes, they evoke feeling that I simply cannot find easily in other ambient music. I need to find more music like this, with a deep forest theme. Do any of you know of any such music?

Check out this thread (Thread 65812) of forest themes. There are plenty of suggestions, but please feel free to add to the discussion with your own picks. Bound to be ambient tracks amidst the others, like Agata Forest from Okami.

By the way, your YouTube links don't work.

I edited my post. The links should work now. I will definitely check that thread out; it could really help me out. Thanks!

If you're looking for things like Brian Eno's Lantern Marsh, it sounds like you might be into dark ambient. Between Interval is a good example of the genre, and Steve Roach has done a bit of dark ambient work. Between Interval is anti-music. It's noise first, some songs have very little rhythm to them, and I'm not sure they even have a key, or a time sig. Here's a good example of what they do; YouTube - Between Interval - the dark light (http://www.youtube.com/watch?v=wHkW8WyJCLQ)

If you want to dig into that genre, Dark Ambient Radio is a good place to start; Dark Ambient Radio (http://www.darkambientradio.de/news.php)