Una forma básica de hacer eso así:
Código C:
Ver originalResponse.Clear();
Response.Buffer = true;
Response.AddHeader("content-disposition", "attachment;filename=[B]FileName.doc[/B]");
Response.ContentEncoding = System.Text.Encoding.UTF7;
Response.ContentType = "application/vnd.word";
System.IO.StringWriter oStringWriter = new System.IO.StringWriter();
System.Web.UI.HtmlTextWriter oHtmlTextWriter = new System.Web.UI.HtmlTextWriter(oStringWriter);
this.GridView1.RenderControl(oHtmlTextWriter);
Response.Output.Write(oStringWriter.ToString());
Response.Flush();
Response.End();