Where can I listen to actual Sumerian/Akkadian/Ancient Mesopotamian
words spoken aloud? (City names, rulers and king, gods and heros,
etc.) Greek and Roman pronunciation would be great also.

I'm a big fan of Mythology and ancient history, and the pronunciation
of the translated words is beyond me.  (The main ones are simple.... 
Zues... Sumer..  Gilgamesh...  The ones we have all heard alot. It's
the names like Enmebaragesi, Lugal-Zage-Si and the like that are the
worst.  I need help with then all though, not just the long ones.)

I've looked at the various guides on the net, and they don't help
much.  Most of the guides I've found are from fiction writers and
metal bands.  Not the best source for proper pronunciation.  I need to
HEAR the words .  Too many of the words are counter intuitive to
normal pronunciation.  Any help would be great.  (Besides personal
use, I intend on adding to the Wikipedia entries as time and desire
allow.)

My wife is a PhD in Ancient Near East studies.  She has studied
Akkadian and Sumerian extensively and is somewhat of an expert on the
topic. So, I will have her write the rest of this:

The fact is that there is nowhere in the world where these languages
are being spoken.  We can only make assumptions (educated assumptions
to be sure, but assumptions nonetheless) about the pronunciation of
most of the words.  We end up using rules from other Semitic languages
to inform our pronunciation and accentuation of these languages that
have never been properly heard by modern ears.  So, with that said,
there are universally accepted pronunciations for most of these words,
let alone a repository online where you could find them.  This is
especially true regarding proper names, which seems to be your primary
interest.  Nonetheless, a good place to start would be the Oriental
Institute at the University of Chicago- it is the leading school of
Assyriology.

I'm sure, however, that you could probablt find something on the Greek
& Roman names, but that is outside of my area of expertise.

I'm sorry to not have better news, but best of luck with your future studies!

Oops, an important sentence should read:

There are NOT universally accepted pronunciations...

Sorry for any confusion:)