As with any tool, you have to know when to use it and when not to.
Like Tehblanx points out that if you want to change the state of a variable that holds an immutable object, you have to create a new object, which can be expensive, especially if the object is big and complex. Absolutely true, but that simply means that you have to intelligently decide which objects should be mutable and which should be immutable. If someone is saying that ALL objects should be immutable, well, that's just crazy talk.
I'd tend to say that objects that represent a single logical "fact" should be immutable, while objects that represent multiple facts should be mutable. Like, an Integer or a String should be immutable. A "Customer" object that contains name, address, current amount, date of last purchase, etc should be mutable. Of course I can immediately think of a hundred exceptions to such a general rule. An exception I make all the time is when I have a class that just exists as a wrapper to hold a primitive in some case where a primitive is not legal, like in a collection, but I need to update it constantly.