Take a look at the javadoc for Collection#add
There's a whole slew of unchecked exceptions mentioned:
Throws:
UnsupportedOperationException - add is not supported by this collection.
ClassCastException - class of the specified element prevents it from being added to this collection.
NullPointerException - if the specified element is null and this collection does not support null elements.
IllegalArgumentException - some aspect of this element prevents it from being added to this collection.
If you have the patience, I'd recommend thoroughly documenting the possible exceptions thrown by your methods this way. In a way, it's even more important to do this for unchecked exceptions, as checked exceptions are somewhat self-documenting (the compiler forces the calling code to acknowledge them).