Static variables in a Web Form are stored in the Cache, so they will persist on a postback. Even though you can, it's probably not the best idea. Just remember that the Cache is not session-scoped, it is available across all sessions.

protected System.Web.UI.WebControls.DataGrid DataGrid1;
protected System.Web.UI.WebControls.LinkButton LinkButton1;
private static DataSet _ds = null;

private void LinkButton1_Click(object sender, System.EventArgs e)
{
    //just here to cause a postback
}

private void Page_Load(object sender, System.EventArgs e)
{
    if(_ds == null)
        SetDataSet();
    DataGrid1.DataSource = _ds.Tables[0].DefaultView;
    DataGrid1.DataBind();
}

private void SetDataSet()
{
    _ds = new DataSet();
    _ds.Tables.Add();
    _ds.Tables[0].Columns.Add();
    _ds.Tables[0].Rows.Add(new object[] {"Hello"});
    _ds.Tables[0].Rows.Add(new object[] {"World!"});
}