If you mean the row number after the last row that is used, you can find it with this:
Dim unusedRow As Long
unusedRow = Cells.SpecialCells(xlCellTypeLastCell).Offset(1, 0).Row
If you mean a row that happens to be blank with data after it... it gets more complicated.
Here's a function I wrote which will give you the actual row number of the first row that is blank for the provided worksheet.
Function firstBlankRow(ws As Worksheet) As Long
'returns the row # of the row after the last used row
'Or the first row with no data in it
Dim rw As Range
For Each rw In ws.UsedRange.Rows
If rw.Address = ws.Range(rw.Address).SpecialCells(xlCellTypeBlanks). _
Address Then
firstBlankRow = rw.Row
Exit For
End If
Next
If firstBlankRow = 0 Then
firstBlankRow = ws.Cells.SpecialCells(xlCellTypeLastCell). _
Offset(1, 0).Row
End If
End Function
Usage example: firstblankRow(thisworkbook.Sheets(1))
or pass any worksheet.
Edit: As ooo pointed out, this will error if there are no blank cells in your used range.