I'm not there yet, but I'm definitely heading that way. I've just moved my filing cabinet to the attic, for the paper I do have to keep, but I'm trying to resist my packrat tendencies and throw away papers I've scanned. I've got a ScanSnap s1500 and it's one of the best things I ever bought.
Like Oogie, OmniFocus looks after my lists and electronic tickler, so there's not much paper around there.
And I blame Barb for making me fall in love with the iPad Mini which has just arrived. I found the bigger iPad a little unwieldy for reading, so often fell back to paper, but I think the iPad Mini will change that, particularly once it's available with a retina display.