I had to do it. I was still 700 posts behind in my Google Reader and it was weighing on me every time I looked at it. So I marked all as read.
I'll still see a lot of posts I missed on my favorite blogs as I move ahead, but sometimes you just have to let go.
I don't know how people with Tivo manage. I could conceivably sit down for a day and catch up on blog posts, but if I were saving TV shows, I'd probably have a year's worth of backlog within short order. The same with magazine subscriptions (The New Yorker, especially).
I quit watching TV entirely a few years ago (and canceled The New Yorker), but I don't think I can quit the Internet.