A set is simply a collection that can contain no duplicates so it sounds perfect for you.
It is also very simple to implement. For example:
Set<String> mySet = new HashSet<String>();
This would provide you a set that can hold Objects of type String.
To add to the set is just as simple:
mySet.add("My first entry!");
By definition of a set, you can add whatever you want and never run into a duplicate.
Have fun!
EDIT : If you decide you are dead-set on using an ArrayList, it is simple to see if an object is already in the list before adding it. For example:
public void addToList(String newEntry){
if(!myList.contains(newEntry))
myList.add(newEntry);
}
Note: All my examples assume you are using String objects but they can easily be swapped to any other Object type.