Combine workbooks

A variation, just 'cuz it's a quiet Saturday:

Sub CombineWorkbooks()
    Dim avsWkb      As Variant
    Dim vsWkb       As Variant
    Dim wks         As Worksheet

    On Error GoTo ErrHandler
    avsWkb = Application.GetOpenFilename(FileFilter:="Excel Files, *.xls", _
                                         MultiSelect:=True, _
                                         Title:="Files to Merge")
    If IsArray(avsWkb) Then
        Application.ScreenUpdating = False

        For Each vsWkb In avsWkb
            With Workbooks.Open(vsWkb)

                For Each wks In .Worksheets
                    If WorksheetFunction.CountA(wks.UsedRange) Then
                        wks.Name = Left(.Name, InStrRev(.Name, ".") - 1) & " " & wks.Name
                        wks.Copy After:=ThisWorkbook.Sheets(ThisWorkbook.Sheets.Count)
                    End If
                Next wks

                .Close SaveChanges:=False
            End With
        Next vsWkb
    Else
        MsgBox "No Files were selected"
    End If

ExitHandler:
    Application.ScreenUpdating = True
    Exit Sub

ErrHandler:
    MsgBox Err.Description
    Resume ExitHandler
End Sub