A remarkably large number of the weapons on a USN warship can be used offensively. Most of the anti aircraft missiles can be used in surface to surface mode. Given their high speed, they can do a large amount of damage, despite the small warhead, simply from KE. This is, in fact, why the US Army is acquiring the Typhon system with SM-6 missiles.

As for the Euro navies, I believe they are generally not designed for really offensive operations. They're generally conceptualized as fighting the Soviets, and so designed for fighting off Russian maritime attack regiments and submarines.