Probably 20% or so freeware, and I don't even know if I have any open-source programs on my primary partition (XP). That said, my web browser (Opera) is freeware, as are my preferred alternatives to it, so I am somewhat reliant on freeware. I could get along with IE (which requires purchasing Windows) if necessary, but it wouldn't be as pleasant. Other freeware includes my PDF viewer, which is rather important for viewing assignments, and various system utilities. I could definitely get by without the system utilities, although they're rather nice to have and save some electric power. And my school's computers have Acrobat Professional (non-free), so I could get along without a free PDF viewer, too.
For music, I use Spiralfrog. It's free, but ad-supported - count it as you will. I could get along without it if necessary, though.
When not web browsing, I spend most of my time using proprietary software - either games, or Microsoft products (whether bundled with Windows or not). I'm pretty satisfied with it.
So I probably use freeware half the time thanks to Opera, and it definitely has improved my computing experience. But most of my software is proprietary and non-free, and I'm happy with that. Although I certainly wouldn't complain if it were free. I just don't have a problem paying for good software if I'll be using it a lot - after all, software developers have to earn a living somehow.
Of course, if you use the [wiki]Richard Stallman[/wiki] definition of freeware, I may well not use freeware at all.
edit: Do you count free web-based IM clients (such as Meebo) as freeware, too? If so, I'm a bit more dependent on freeware than I'd stated above, although I could certainly switch back to cell phone only if necessary.