ArrayLists (or, in general, the Collections) are intended for heavy read and write operation without thinking too much about capacity, extension and so forth (in the first place). It is much more comfortable to call ArrayList#add than creating a new array with size oldArray.length + 1, doing a System.arraycopy and adding then the element. There are lots of handy methods (indexOf, remove, sublist) which leverage the complexity of use in comparison to arrays.
If you take a look at the Collections class, you'll find a lot of convenience methods like shuffle or reverse.
The use of List in general is much more common than arrays, except you're heading for performance.