Function to count number of lines in a text file

Too large files...
The following is the fastest-effeciently way I know of:

Dim oFso, oReg, sData, lCount
Const ForReading = 1, sPath = "C:\file.txt"
Set oReg = New RegExp
Set oFso = CreateObject("Scripting.FileSystemObject")
sData = oFso.OpenTextFile(sPath, ForReading).ReadAll
With oReg
    .Global = True
    .Pattern = "\r\n" 'vbCrLf
    '.Pattern = "\n" ' vbLf, Unix style line-endings
    lCount = .Execute(sData).Count + 1
End With
WScript.Echo lCount
Set oFso = Nothing
Set oReg = Nothing

The only alternative I see is to read the lines one by one (EDIT: or even just skip them one by one) instead of reading the whole file at once. Unfortunately I can't test which is faster right now. I imagine skipping is quicker.

Dim objFSO, txsInput, strTemp, arrLines
Const ForReading = 1
Set objFSO = CreateObject("Scripting.FileSystemObject")

strTextFile = "sample.txt"
txsInput = objFSO.OpenTextFile(strTextFile, ForReading)

'Skip lines one by one 
Do While txsInput.AtEndOfStream <> True
    txsInput.SkipLine ' or strTemp = txsInput.ReadLine
Loop

wscript.echo txsInput.Line-1 ' Returns the number of lines

'Cleanup
Set objFSO = Nothing

Incidentally, I took the liberty of removing some of your 'comments. In terms of good practice, they were superfluous and didn't really add any explanatory value, especially when they basically repeated the method names themselves, e.g.

'Create a File System Object
... CreateObject("Scripting.FileSystemObject")

You could try some variation on this

cnt = 0
Set fso = CreateObject("Scripting.FileSystemObject")
Set theFile = fso.OpenTextFile(filespec, ForReading, False)
Do While theFile.AtEndOfStream <> True
   theFile.SkipLine
   c = c + 1
Loop
theFile.Close
WScript.Echo c,"lines"

If somebody still looking for faster way, here is the code:

Const ForAppending = 8
Set fso = CreateObject("Scripting.FileSystemObject") 
Set theFile = fso.OpenTextFile("C:\textfile.txt", ForAppending, Create:=True) 
WScript.Echo theFile.Line 
Set Fso = Nothing

Of course, the processing time depend very much of the file size, not only of the lines number. Compared with the RegEx method TextStream.Line property is at least 3 times quicker.