My twins were reading by three as well (as was I, come to think of it). Lots of reading to them, but we also made a game where my wife or I would change random words or names in the books we were reading. We'd start off doing it to a story they knew very well and for humour (ie: Humpty Dumpty sat on a pig...), and gradually work our way to more subtle changes in books we hadn't read before. We knew they were reading along when thay caught us out.
Also Reader Rabbit and other reading games. Lots available for PC, Mac, etc. Vtech Leapster handhelds have some great reading and math games as well. I haven't looked into what's available for iOS or Android lately, but a couple of years ago there wasn't much that weren't "read along" stories. Things may have changed.