Hi William,
 
 WB> I have a 386 with an ordinary Serial Port.  Currently, I 
 WB> have a 2400 modem and I am thinking of buying a faster one. 
 WB> Could anyone tell me the maximum speed of modem which 
 WB> would work with my computer.

A 386 can handle a 16550 UART if you want to upgrade that for a little cash,
that will get you a max of 115200 port speed with 33.6K modems working fine
on this.
On an ordinary 8250 or 16450 (what you most probably have), you can squeeze
a maximum of 19200 port speed, 14.4K modems or lower working on this speed.
A 28.8K/33.6K will work but there will be overruns and data will most
probably be lost.

l8r

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