Well, I got it working.

Sub Convert2Text()
    Dim i As Integer, k As Integer, n As Integer, m As Integer
    Dim Rng As Range, Dpath As String
    Dim FSO As Scripting.FileSystemObject
    Dim TxtFile As TextStream
    Dim MaxLen As Integer

        Set Rng = Application.InputBox("Please Select range.", "-Convert to Text-", , -Range("R2").Left, Range("R2").Top, , , 8)
        If Rng Is Nothing Then
            Exit Sub
        End If
        Dpath = Environ("USERPROFILE") & "\Documents\"
        Set FSO = New FileSystemObject
        Set TxtFile = FSO.CreateTextFile(Dpath & "Outputfile.txt", True)

            MaxLen = 1
            For i = 1 To Rng.Columns.Count
                For k = 1 To Rng.Rows.Count
                If MaxLen < Len(Rng.Cells(i, k)) Then
                    MaxLen = Len(Rng.Cells(i, k))
                End If
                Next k
            Next i
            MaxLen = MaxLen + 4

            For i = 1 To Rng.Columns.Count
                TxtFile.Write "+"
                    For m = 1 To MaxLen
                        TxtFile.Write "="
                    Next m
            Next i
                TxtFile.Write "+"
                TxtFile.WriteLine

            For n = 1 To Rng.Rows.Count
                For i = 1 To Rng.Columns.Count
                        TxtFile.Write "|"
                        TxtFile.Write " "
                        TxtFile.Write " "
                        TxtFile.Write Rng.Cells(n, i)

                        For k = 1 To MaxLen - (Len(Rng.Cells(n, i))) - 2
                            TxtFile.Write " "
                        Next k
                Next i
                        TxtFile.Write "|"
                        TxtFile.WriteLine

                For i = 1 To Rng.Columns.Count
                        TxtFile.Write "+"
                            For m = 1 To MaxLen
                                TxtFile.Write "-"
                        Next m
                Next i
                        TxtFile.Write "+"
                        TxtFile.WriteLine
            Next n

        MsgBox "Done!"
        Shell "explorer.exe " & Dpath, vbNormalFocus

End Sub

Now, I have to focus on getting the numbers right aligned. Thank you all for your suggestions.

The problem is not that the file format is not supported - These are all plain vanilla ASCII text files. My problem is the obligatory link between ASCII text files and the extension *.txt.

I am working in structural bioinformatics, and specialized programs I use to generate these files require different extensions: e.g. *.pdb for atom coordinates, *.seq for nucleotide sequences,*.aln for multisequence alignments, *.rsa for residue accessibility, *.ddG for energy changes upon mutation  ...

While I can import all of these programmatically through home-spun vba macros, no longer being able to just specify that I want to open one of these files e.g. as a fixed format or delimited text file independent of the file extension is a bloody nuisance.