Hi,
It depends whether you mean "genuine RS232" (typically +/- 10 volt levels) from a chip such as the MAX232, or only the 5 volt "RS232-TTL" (or the "inverted RS232-TTL" of the PICaxe Programming/Debug interface) used as a "local" interface by many microcontrollers (e.g. to a MAX232).
The "official" RS232 specification gives a maximum range of 15 metres (50 feet) with a 2500 pF cable capacitance at 19200 baud, but Cat5 cable is only around 50pF/m which could get to 50 metres. Then halving the baud rate may double the range, so 4800 baud (as used by PICaxe SERTXD/RXD) might get beyond 150 metres, but it rather depends on the "environment" (i.e. Noise/Interference, etc.).
In a very (electrically) "clean/quiet" environment then even 5 volt (TTL) signals might be sufficient (at around 2400 baud), but if "interface" chips need to be added, then probably a balanced configuration such as RS485 might be a better choice than a MAX232.
Cheers, Alan.