Hi,
Depends on the 'serial programmer' in question, and the type of microcontroller you're planning on programming. Many programmers for PIC's, such as the 'JDM' programmer, use the +/- 12v from the serial port to generate the 13v+ necessary to put the micro in 'programming mode'. However, as bbgil stated, USB<->Serial cables, don't always produce a +/- 12v swing on the outputs, and therefore, do not always generate sufficient voltage for the serial port programmer to work.
That said, if you rpogrammer simply uses the 'data' from the serial port, and is powered externally, I imagine a USB/serial cable would work. Certain 'serial programmers' can be modified so that they can use external power (+15V usually) so the serial cables I/O's are buffered, so thye will work at low level, non-RS232 voltages, such as 0-5V.
Please provide more information, such as your microntroller, and the programmer.
BuriedCode.