Assuming you're talking about the cost of using the Serializable
attribute rather than the actual serialization process, one drawback would be that a third party would normally assume that the class is designed to be serializable. Whilst this may be the case, if you're just marking it serializable for the sake of it (and if there's a chance a third party might interact with it), then you'd probably want to spend time ensuring that the class is suited to be serialised in an efficient manner. So it's more of a resource tradeoff than a technical one, from that point of view.
From a technical standpoint, as Marc Gravell said, just using the attribute won't really have any overhead.