Depending on the database you are using you can use ADO in VB or ASP (or any other COM-compliant language for that matter).
Set a reference to Microsoft ActiveX Data Objects x.x Library, if you don't have this for some reason you can download it from microsoft search for MDAC.
Code:
Dim objConn as New ADODB.Connection
Dim strSQL as String
Dim strConn as String
strConn = "Provider=Microsoft.Jet.OLEDB.4.0; Data Source=C:\foldername\filename.mdb" 'Connection string for an access database, string will be different for different databases
strSQL = "DELETE * FROM tablename WHERE dateExpireFieldName <" & date()
'Open Connection
objConn.Open strConn
'Execute SQL Statement
objConn.Execute strSQL
'Close Connection
objConn.Close
Set objConn = Nothing