Forse puoi usare quest'API:
Declare Function GetClipboardData Lib "user32" (ByVal wFormat As Long) As Long

Per VB.Net è:
System.Windows.Forms.Clipboard


Questo è un esempio che ho trovato sul sito http://www.allapi.net/apilist/GetClipboardData.shtml :

codice:
Private Const CF_TEXT = 1
Private Declare Function GetClipboardData Lib "user32" (ByVal wFormat As Long) As Long
Private Declare Function CloseClipboard Lib "user32" () As Long
Private Declare Function OpenClipboard Lib "user32" (ByVal hwnd As Long) As Long
Private Declare Function lstrlen Lib "kernel32" Alias "lstrlenA" (ByVal lpString As Long) As Long
Private Declare Sub CopyMemory Lib "kernel32" Alias "RtlMoveMemory" (pDst As Any, pSrc As Long, ByVal ByteLen As Long)
Private Sub Form_Load()
    'KPD-Team 2001
    'URL: http://www.allapi.net/
    'E-Mail: KPDTeam@Allapi.net
    Dim hStrPtr As Long, lLength As Long, sBuffer As String
    OpenClipboard Me.hwnd
    hStrPtr = GetClipboardData(CF_TEXT)
    If hStrPtr <> 0 Then
        lLength = lstrlen(hStrPtr)
        If lLength > 0 Then
            sBuffer = Space$(lLength)
            CopyMemory ByVal sBuffer, ByVal hStrPtr, lLength
            MsgBox sBuffer, vbInformation
        End If
    End If
    CloseClipboard
End Sub
Spero che ti sarà utile (ora lo leggo anch'io ).
Ciao!