What effect, if any, do different fabrics have on the generation of
static electricity?

A LOT!

Fabrics like rayon and wool tend to generate a lot of static
electricity, while other fabrics like linen tend to generate
significantly less.  This of course assumes that all other variables
are constant...

There are plenty of other factors in static electricity generation,
including humidity, amount of motion, and so on...

To minimize static electricity, many clothing manufacturers recommend
using a fabric softener designed to reduce static electricity, such as
Bounce.  Of course, you have to make sure that you are careful your
clothes do not become damaged from the dryer...

Some starting ideas for you:

1) Walking across a carpet is one of the primary ways the doorknob
shock is generated.

2) Wool generates so much static electricity from friction that it can
cling to the body and other fabric

3) Some synthetic clothing generates electricity

4) Cotton does not generally generate charge. For that reason bed
clothes and under--wool clothing should be cotton. One problem with
cottom is that it absorbs humidity, and in certain environments the
cooling of collected sweat can lead to hypothermia.

If you are inquiring for a physics viewpoint, then you can rub a glass
or plastic rod with "rabbit skin". You should remember this from
physics. There is a table you can look for which will rate on how much
electricity is produced on rubbing a glass rod.