How is the supply to your board arranged and what additional I/O do you have connected to it that is connected to external devices? If you have a properly designed supply (using an isolated transformer) AND the only ground interconnection you have between your board and the PC is through the RS232 port, little problems can occur.

Galvanic separation of the RS232 signal is a (good) solution. The MAX251 + compatibles are quite expensive; a cheaper alternative would be to use a couple of optocouplers in combination with a galvanically separated miniature DC/DC converter to supply the driver (MAX232 or similar).