Apache Storm guarantees every tuple will be fully processed. One of Apache Storm's core mechanisms is the ability to track the lineage of a tuple as it makes its way through the topology in an extremely efficient way. Read more about how this works here.
Apache Storm's basic abstractions provide an at-least-once processing guarantee, the same guarantee you get when using a queueing system. Messages are only replayed when there are failures.
Using Trident, a higher level abstraction over Apache Storm's basic abstractions, you can achieve exactly-once processing semantics.