A PIC for instance does not have a FIFO for its standard serial port module. You get a byte in a register and if you are not fast enough before the next byte is ready things might go wrong. Of course writing the PIC formware in such a way that it can always deal with the maximum input rate (for instance 9600 baud => ~1ms per byte) is the real art here. Also you can consider handshaking too, although the PIC module does not have this automatically.
Rolf Kalbermatter