I want to clarify some things here for the original poster which others have alluded to but haven't really explicitly stated. When you say that you want a Unique List, that is the very definition of an Ordered Set. Some other key differences between the Set Interface and the List interface are that List allows you to specify the insert index. So, the question is do you really need the List Interface (i.e. for compatibility with a 3rd party library, etc.), or can you redesign your software to use the Set interface? You also have to consider what you are doing with the interface. Is it important to find elements by their index? How many elements do you expect in your set? If you are going to have many elements, is ordering important?
If you really need a List which just has a unique constraint, there is the Apache Common Utils class org.apache.commons.collections.list.SetUniqueList which will provide you with the List interface and the unique constraint. Mind you, this breaks the List interface though. You will, however, get better performance from this if you need to seek into the list by index. If you can deal with the Set interface, and you have a smaller data set, then LinkedHashSet might be a good way to go. It just depends on the design and intent of your software.
Again, there are certain advantages and disadvantages to each collection. Some fast inserts but slow reads, some have fast reads but slow inserts, etc. It makes sense to spend a fair amount of time with the collections documentation to fully learn about the finer details of each class and interface.