No, there's no split-screen mode. Online only.
What is with all the hate this game has been getting? The last games I bought on release were Halo: Reach, Fallout: New Vegas, Portal 2, and now Dead Island.
Out of all of those, Dead Island is the only one I feel was good value for the money I spent. I really did enjoy Portal 2, but is was a bit short for a full priced game, and as someone who bought it on day one, the temporary twenty dollar price drop in the second week of its release felt like a big fat middle finger obnoxiously waving itself in my face. :-(
So far my experience of Dead Island (which has been a couple of hours solo and several hours co-op) has been an extremely fun one. After several hours of playing, my game has frozen solid on me twice, in comparison to FO:NV which would freeze about once every hour, this really isn't that big of a deal to me. The only other glitches I have found are an occasional vanishing zombie, weird and annoying, but not anything close to a game breaker.
The game feels a lot like Borderlands with depth, Fallout 3 with co-op, and Left 4 Dead with freedom. A very pleasant mix, and one of the best and most enjoyable games I have played in a long time. I really like having run-ins with the occasional human enemy as well. To me that adds a whole lot to the game.