I don't, really, but I do kind of know how you feel. If the Internet goes out, I feel really lost and disconnected (heh) from the rest of... well, everything, even though most of my time is spent on IRC and IM programs. I tend to feel weird, even guilty, if I'm not signed into them.
But yeah, you can't just "quit" cold-turkey. Try to limit your time to say... 4 hours a day to start. If you say "large chunk of waking hours" and you also have school, I'm just going to assume you're online for 8 hours minimum (this was very common for me during school as well, usually it was more depending on class schedule). Cut your use in half, but take it in chunks if you need to when you start. Maybe spend an hour online, then unplug your router and watch anime offline, or play a video game offline.
I really don't have much advice except to try it in baby steps, and maybe shutting your Internet/computer off when you're not online, if you feel that would help.