How to: Sort ListView Items
http://msdn.microsoft.com/en-us/library/ms229643(VS.80).aspx

class ListViewItemComparer : IComparer
{
    private int column;
    public ListViewItemComparer() : this(0) {}
    public ListViewItemComparer(int column)  
    {      
        this.column = column;
     }
     
    public int Compare(object x, object y) // string compare
    {       
          return String.Compare(((ListViewItem)x).SubItems[column].Text,  
                                       ((ListViewItem)y).SubItems[column].Text);
   }
}

/////
public partial class Form1 : Form
{
[…]
private void listView1_ColumnClick(object sender, ColumnClickEventArgs e)
{
           
   // Set the column number that is to be sorted; default to ascending.            
   this.listView1.ListViewItemSorter = new ListViewItemComparer(e.Column);
           
   // Perform the sort with these new sort options.
   this.listView1.Sort();
}
}