I've noticed a lot of confusion about what type of unchecked exception is the right one to throw under various circumstances. Here's a very simple explanation of the most common types.
NullPointerException - multiple schools of thought on this one. Of course, it's thrown automatically by the runtime when you try to dereference null. Many say that you should never rely on this behavior, and should always check for null explicitly. Many also believe that when you find a null reference, you should throw IllegalArgumentException instead of NPE. This way, a thrown NPE always indicates some programming error in the implementation of the method, not a failure of the caller to pass valid parameters. I'm not taking a stand on this issue right now.
IllegalArgumentException - throwing this exception implies that there exists at least one other value for this parameter that would have caused the check in question to pass. If the caller can't remedy this exception by substituting another value for the argument in question, it's the wrong exception to throw. Note that in some of these cases IndexOutOfBoundsException is more appropriate (and strangely, IOOBE doesn't extend IAE).
IllegalStateException - this exception implies that there are no argument values that could have caused the check to succeed, yet, there does exist at least one alternate state that the instance in question could have been in, which would have passed the check. Note that this type almost never makes sense for a static method, unless you rely heavily on static state (shame on you). Note also that this exception is appropriate whether or not it is possible to actually mutate this aspect of the instance's state, or it's already too late.
UnsupportedOperationException - this means that the method invoked will always fail for an instance of this class (concrete type), regardless of how the instance was constructed.
AssertionError - this is the right exception to use whenever a statement should by rights be impossible to reach.
I hope this helps. Any points you want to argue?