I have built a circuit with a PIC 16F627 and a MAX232CPE, I use the hardware USART on the PIC, which is connected to the MAC232CPE (RS232 chip).
Now I want to add two status LEDs to the RX and TX, so that when the line goes high (logic high), the LEDs lights up. I don't want to put anything in there to affect coms between the chips.
Just resistors and LED's on the lines, certainly the PIC is well able to drive a LED, and the MAX232 should be OK as long as you don't try and draw excessive current off of it - so don't run the LED's too bright.
You used to be able to buy RS232 monitors (and probably still can?), which plugged in the RS232 side and had LED's for all lines - I've still got one.