Given:

Element[] array = new Element[] { new Element(1),new Element(2),new Element(3) };

The simplest answer is to do:

List<Element> list = Arrays.asList(array);

This will work fine. But some caveats:

1. The list returned from asList has fixed size. So, if you want to be able to add or remove elements from the returned list in your code, you'll need to wrap it in a new ArrayList. Otherwise you'll get an UnsupportedOperationException.
2. The list returned from asList() is backed by the original array. If you modify the original array, the list will be modified as well. This may be surprising.

Since this question is pretty old, it suprises me that nobody suggested the simplest form yet:

List<Element> arraylist = Arrays.asList(new Element(1),new Element(2),new Element(3));

As of Java 5, Arrays.asList() takes a varargs parameter and you don't have to construct the array explicit.

new ArrayList<T>(Arrays.asList(myArray));

^{(old thread, but just 2 cents as none mention Guava or other libs and some other details)}

If You Can, Use Guava

It's worth pointing out the Guava way, which greatly simplifies these shenanigans:

Usage

For an Immutable List

Use the ImmutableList class and its of() and copyOf() factory methods ^{(elements can't be null)}:

List<String> il = ImmutableList.of("string", "elements");  // from varargs
List<String> il = ImmutableList.copyOf(aStringArray);      // from array

For A Mutable List

Use the Lists class and its newArrayList() factory methods:

List<String> l1 = Lists.newArrayList(anotherListOrCollection);    // from collection
List<String> l2 = Lists.newArrayList(aStringArray);               // from array
List<String> l3 = Lists.newArrayList("or", "string", "elements"); // from varargs

Please also note the similar methods for other data structures in other classes, for instance in Sets.

Why Guava?

The main attraction could be to reduce the clutter due to generics for type-safety, as the use of the Guava factory methods allow the types to be inferred most of the time. However, this argument holds less water since Java 7 arrived with the new diamond operator.

But it's not the only reason (and Java 7 isn't everywhere yet): the shorthand syntax is also very handy, and the methods initializers, as seen above, allow to write more expressive code. You do in one Guava call what takes 2 with the current Java Collections.

If You Can't...

For an Immutable List

Use the JDK's Arrays class and its asList() factory method:

List<String> l1 = Arrays.asList(anArrayOfElements);
List<String> l2 = Arrays.asList("element1", "element2");

Note that the returned type for asList() says ArrayList, but it's not java.util.ArrayList. It's an inner type, which copies ArrayList but actually directly references the past array and forbis modifications. See the next step if you need a mutable list.

For a Mutable List

Same as above, but wrapped with an actual java.util.ArrayList:

List<String> l1  = new ArrayList<String>(Arrays.asList(array));    // Java 1.5 to 1.6
List<String> l1b = new ArrayList<>(Arrays.asList(array));          // Java 1.7+
List<String> l2  = new ArrayList<String>(Arrays.asList("a", "b")); // Java 1.5 to 1.6
List<String> l2b = new ArrayList<>(Arrays.asList("a", "b"));       // Java 1.7+

For Educational Purposes: The Good ol' Manual Way

// for Java 1.5+
static <T> List<T> arrayToList(final T[] array) {
  final List<String> l = new ArrayList<String>(array.length);

  for (final String s : array) {
    l.add(s);
  }
  return (l);
}

// for Java < 1.5 (no generics, no compile-time type-safety, boo!)
static List arrayToList(final Object[] array) {
  final List l = new ArrayList(array.length);

  for (int i = 0; i < array.length; i++) {
    l.add(array[i]);
  }
  return (l);
}

Another way (although essentially equivalent to the new ArrayList(Arrays.asList(array)) solution performance-wise:

Collections.addAll(arraylist, array);

You probably just need a List, not an ArrayList. In that case you can just do:

List<Element> arraylist = Arrays.asList(array);