|Why are pull-up resistors used?  I am interfacing a keypad to a
|PIC16C84, I understand I can set the internal pull up resistors but I am
|not sure why they are needed.

|Typically what value would I use for an external pull-up?

First of all, because Microchip saw the need for pull-ups in certain
applications, they provided a handy feature which can connect pull-ups
to all of the PortB pins internal to the PIC, obviating the need for
external pull-ups in many cases.  Clearing bit 7 of the option register
will enable pull-ups on all PORTB pins that are set for input.

That having been said, pull-ups are a means of ensuring that a signal
that is not actively being driven will assume a default "high" state;
pull-downs cause such signals to assume a default "low" state.  When
scanning keyboards and such, the normal condition of the input wires is
that nothing is connected to them (unless a key is pressed).  Using a
pull-up resistor will ensure that the input is at a known (high) state.
Otherwise, the input's behavior when nothing is connected is unpredict-
able(*).

(*) There is a trick for keyboard scanning on the PIC which may allow you to
    avoid using pull-ups, and which may also provide for somewhat more-robust-
    than-normal detection of kepresses when the key contacts are dirty.  It
    does, however, require that keys be scanned and detected multiple times to
    avoid false hits.  Here's the trick, assuming a 4x4 keyboard wired with rows
    on PORTB4-7 and columns on PORTB0-3.

        Set PORTB all to actively-driven high
   Float PORTB0-3 and ground one of PORTB4-7
   Read PORTB0-3.  Any pins that have gone low currespond to
     likely-pressed buttons on the row you just grounded.
   Set PORTB to all actively-driven low
   Float PORTB0-3 and drive one of PORTB4-7 high.
   Read PORTB0-3.  Any pins that have gone high correspond to
     likely-pressed buttons on the row you just drove high.

   By repeating this procedure with each row on PORTB4-7, you can scan the
   entire keyboard.  Any key whose CAPACITANCE is substantially greater than
   the PIC's port pin's capacitance and that of un-pressed keys on its column
   will be detected even if the contact is poor.  Adjusting the amount of time
   before the "read"s wll change the sensitivity of the device; with a bit of
   effort, excellent reliability should be obtainable.  Note, though, that any
   keyboard designed with this approach should be tested in conditions of vari-
   able humidity since humid environments may cause false-tripping if the device
   is too sensitive.