had better be List
The only List implementation in java.util.concurrent is CopyOnWriteArrayList. There's also the option of a synchronized list as Travis Webb mentions.
That said, are you sure you need it to be a List? There are a lot more options for concurrent Queues and Maps (and you can make Sets from Maps), and those structures tend to make the most sense for many of the types of things you want to do with a shared data structure.
For queues, you have a huge number of options and which is most appropriate depends on how you need to use it:
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