In Neil Gaiman's "American Gods", there is one "old world" god he
represents as living in Las Vegas and being entirely forgettable.  I
would like to know who this god represents, and any short background
mythology you can find about him including what culture he came from
and stories about him, if available.

The god appears briefly early in the novel, and starting on page 221
Shadow and Wednesday go to visit the god at his home in Las Vegas. 
Here are some descriptions of the god:

"His charcoal gray suit is immaculate, his hair is dark, he is
clean-shaven, and his face and his demeanor are, in every sense,
forgettable.  None of the other men has even observed that he is
there, or if they have noticed him, they have forgotten him on the
instant."

The god seems attracted to money and transactions, and the people
losing money gambling in Vegas are making sacrifices to him:

"The man in the charcoal suit ... feeling the flow of the money
through the town.  In his mind the movement of money forms a fine
latticework, a three dimensional cat's cradle of light and motion. 
What he finds attractive about this desert city is the speed of
movement, the way the money moves from place to place and hand to
hand: it's a rush to him, a high, and it pulls him like an addict to
the street."

Later on: "The man ... sips his Laphroaig and water, savoring the
marshy taste, the body-in-the-bog quality of the whiskey."  Later on
wednesday offers him a soma, "the real stuff."

Finally, the man tells a waitress where to be in the future to make
money by "following the golden threads in his mind," and seeing a node
where money will be.

So overall there are several hints here.  "Soma" seems to be the drink
of the Hindu gods, and the Hindu god of wealth is Kubera, but I can
find nothing that would explain why the god is so forgettable - this
forgettableness seems to be the main aspect of this god.  The god
seems able to meddle in affairs of humans dealing with money and can
slip by unnoticed.

So basically if you can figure out which god this represents that
would answer my question.  Thanks!

My theory is that the "Forgettable God" is Pluto, also known as Hades.
He is the only god I know of who is associated both with money and
with forgetfulness.

Pluto is both the god of wealth and the lord of the underworld, where
the spirits of the dead dwell. In the land of the dead, there is a
river, called Lethe. When men drink from this stream, they forget
their pasts.

Here's a bit of info about Lethe:

"Lethe... In ancient Greek mythology, one of the several rivers of
Hades. Drinking from the river Lethe {'(river of) forgetfulness' or
'oblivion') caused complete forgetfulness. Some ancient Greeks
believed that souls were made to drink from the river before being
reincarnated, so they would not remember their past lives."

Wikipedia
http://www.wikipedia.org/wiki/Lethe

And some info on Pluto:

"Hades (Pluto) was the brother of Zeus. He was made lord of the
underworld, ruling over the dead. He was a greedy god who was greatly
concerned with increasing his subjects... He was also the god of
wealth, due to the precious metals mined from the earth. He had a
helmet that made him invisible."

Classics Unveiled
http://www.classicsunveiled.com/mythnet/html/olympian.html#Hades

I am posting this as a comment, rather than as an answer, since I do
not believe it can be proven for certain who the "Forgettable God" is;
Neil Gaiman has thus far remained silent on the matter.