Try this. It's killo's code, but slightly modified. It now saves the files with their original names. You also have to specifiy a new key for each file or you'll get an error saying the key already exists in the collection.

Code:
Private Sub Form_Load()
Dim tmp() As String
Dim i As Integer
Open App.Path & "\links.txt" For Input As #1
    tmp() = Split(Input(LOF(1), 1), vbCrLf)
Close #1
For i = 0 To UBound(tmp)
DL.Download tmp(i), App.Path & "\" & ExtractFileName(tmp(i)), "k" & i
Label2.Caption = "Connecting..."
Next i
End Sub

Private Function ExtractFileName(ByVal vStrFullPath As String) As String
   Dim intPos As Integer
   intPos = InStrRev(vStrFullPath, "/")
   ExtractFileName = Mid$(vStrFullPath, intPos + 1)
End Function