A simple merge function

First I ask if you really want to change the data or create a 'better' way to view the data. I ask because often people treat excel sheets as data collection, storage and viewing when often it is better to have data collection and storage set up separate from data viewing. For example, that is why Excel has Pivot Tables. By the way, you might consider if a Pivot Table view might be adequate for what you want. If not, some the new Dynamic Array formulas could be used to generate a view that you want.
That all said, if you want to change the data (i.e. use VBA) then I might suggest a slight variation on your pseudo-code:

Sub mergeDups()
  Dim i, FoundRow, C, LastRow, LastCol As Long
  With ActiveSheet
    LastRow = .UsedRange.Rows.Count
    LastCol = .UsedRange.Columns.Count
    For i = LastRow To 1 Step -1
      For FoundRow = 1 To i
           If (.Cells(i, 1) = .Cells(FoundRow, 1)) Then Exit For
       Next FoundRow
      If (FoundRow < i) Then
         For C = 2 To LastCol
              If InStr(1, .Cells(FoundRow, C).Value2, .Cells(i, C).Value2) = 0 Then
                     .Cells(FoundRow, C).Value2 = .Cells(FoundRow, C).Value2 & ", " & .Cells(i, C).Value2
              End If
         Next C
          .Cells(i, 1).EntireRow.Delete
       End If
    Next i
  End With
End Sub