Here is a slight variation on Shimmy's one for collection of classes that already implement the well-known IComparable<T> interface. In this case, the "order by" selector is implicit.

public class SortedObservableCollection<T> : ObservableCollection<T> where T : IComparable<T>
{
    protected override void OnCollectionChanged(NotifyCollectionChangedEventArgs e)
    {
        base.OnCollectionChanged(e);
        if (e.Action != NotifyCollectionChangedAction.Reset &&
            e.Action != NotifyCollectionChangedAction.Move &&
            e.Action != NotifyCollectionChangedAction.Remove)
        {
            var query = this.Select((item, index) => (Item: item, Index: index)).OrderBy(tuple => tuple.Item, Comparer.Default);
            var map = query.Select((tuple, index) => (OldIndex: tuple.Index, NewIndex: index)).Where(o => o.OldIndex != o.NewIndex);
            using (var enumerator = map.GetEnumerator())
            {
                if (enumerator.MoveNext())
                {
                    base.MoveItem(enumerator.Current.OldIndex, enumerator.Current.NewIndex);
                }
            }
        }
    }

    // (optional) user is not allowed to move items in a sorted collection
    protected override void MoveItem(int oldIndex, int newIndex) => throw new InvalidOperationException();
    protected override void SetItem(int index, T item) => throw new InvalidOperationException();

    private class Comparer : IComparer<T>
    {
        public static readonly Comparer Default = new Comparer();

        public int Compare(T x, T y) => x.CompareTo(y);
    }

    // explicit sort; sometimes needed.
    public virtual void Sort()
    {
        if (Items.Count <= 1)
            return;

        var items = Items.ToList();
        Items.Clear();
        items.Sort();
        foreach (var item in items)
        {
            Items.Add(item);
        }
        OnPropertyChanged(new PropertyChangedEventArgs("Item[]"));
        OnCollectionChanged(new NotifyCollectionChangedEventArgs(NotifyCollectionChangedAction.Reset));
    }
}