Extending multiple classes was primarily left out in order to keep Java "simple." The main problem which programmers could encounter with being able to extend multiple classes is the Diamond Problem (which I prefer to call the Dastardly Diamond of Death) When extending multiple classes it creates a serious possibility of ambiguity in your method calls/classes. The reason why multiple interfaces are allowed to be implemented is that you must override all methods provided by the interfaces you are implementing. While you can still have odd naming problems with multiple interfaces the forced override of all methods in the implementing class helps to limit all the pitfalls of extending multiple classes.
There was an old entertaining article about interfaces and why Java developers decided to go the route the did, I will edit my post if I come across it again.