JJ writes:

I would like to construct a very simple footbridge over our creek.
The distance is around 12-14 feet from bank to bank. I figured on
using two 16' pieces of lumber as the support (about 18-20 inches
apart), with 1x6 decking boards along the top. About 2.5' to 3' wide.

My question is what should I use for the support beams. I don't want
it to get too high off the ground, because we would like to easily ski
over it in the winter.

I was conteplating either using 4x6 lumber or 2x8 lumber. I'm not
sure which will provide a stiffer bridge - which is what I want. How
much weight can I expect such a bridge to hold? Should I be using a
third support beam?

If you are thinking of spanning the gap with lumber laid straight
across, I'd forget that right away.

You need to construct a triangle shaped support then span the
gap with lumber hung from the triangle:


*
* *
* *
==*===========*==
* *

4x4s (*) and 2x6s (=) would probably do the job.
You need to plant the 4x4s in cement.