private void textBox1_DragEnter(object sender, DragEventArgs e)
        {
            if (e.Data.GetDataPresent(DataFormats.FileDrop))
            {
                e.Effect = DragDropEffects.All;
            }
            else
            {
                e.Effect = DragDropEffects.None;
            }
        }

        private void textBox1_DragDrop(object sender, DragEventArgs e)
        {
            String[] files = (String[])e.Data.GetData(DataFormats.FileDrop, false);
            if (files.Length > 0)
            {
                textBox1.Text = files[0];
            }
        }

------解决方案--------------------

public partial class Form1 : Form
   {
       public Form1()
       {
           InitializeComponent();

           this.textBox1.Multiline = true;
           this.textBox1.AllowDrop = true;
           this.textBox1.DragDrop+=new DragEventHandler(textBox1_DragDrop);
           this.textBox1.DragEnter+=new DragEventHandler(textBox1_DragEnter);
       }

       protected void textBox1_DragEnter(object sender, System.Windows.Forms.DragEventArgs e)
       {
           IDataObject dataObject = e.Data;
           if (dataObject.GetDataPresent(DataFormats.FileDrop))
           {
               e.Effect = DragDropEffects.Copy;
           }
       }

       protected void textBox1_DragDrop(object sender, System.Windows.Forms.DragEventArgs e)
       {
          
           IDataObject dataObject = e.Data;

           if (dataObject == null) return;

           if (dataObject.GetDataPresent(DataFormats.FileDrop))
           {
               string[] files = (string[])dataObject.GetData(DataFormats.FileDrop);

               foreach (string file in files)
               {
                   System.IO.FileInfo fi = new System.IO.FileInfo(file);
                    this.textBox1.Text += "文件名：" + fi.Name;
                  
               }

           }
       }

   }