Jawa or Ewoks... way too silly. I guess with canononlyplz approach one would have to use any species one can think of, but I prefer at least some EU.
I'll go through (most of the) original post civs here:
Ancient Old Republic
Leaders: Carth Onasi, Bastila Shan (from KOTOR 1 and 2)
UU:
Just "Old Republic" might be better
Leaders:
This guy might be the only one I know of and he doesn't have a name. You can do better than Carth and Bastila however. Pick that admiral woman from KotOR, for example. Something Dodonna?
Galactic Senate (from the prequels)
Leaders: Chancellor Palpatine
UU:
Galactic Republic
Leaders: Chancellors Palpatine and
Finis Valorum
Stormtrooper could be a good UU for Empire
Mandalorians
Leaders: Mandalore (real name Canderous Ordo)
UU:
There are several
Mandalores to be chosen from. Indomitable and Ordo are probably the most familiar ones for public. Fett wasn't so much into it.
UU:
Basilisk war droid
Quarren? Odd choice, Mon Cals would be better.
Sith Empire
Leaders: Darth Malak, Darth Nihilous
UU:
You could represent the Sith from a wider period of time than just KotOR. Pick 2 leaders from: Naga Sadow, Exar Kun, Darth Revan and Lord Kaan. Malak wasn't as great leader as Revan and Nihilus was more of a force of nature than a leader at all.
Rebel Alliance
Leaders: Mon Mothma, Princess Leia
UU:
More leader options: Ackbar, Jan Dodonna, Bail Organa. Personally I'd move Leia to NR.
UU: Wookie warband maybe; a powerful infantry unit.
Chiss Empire
Leaders: Grand Admiral Thrawn
UU:
Chiss
Ascendancy
Leader:
Aristocra Chaf'orm'bintrano (Formbi)
Can't blame you for using the more familiar Mitth'raw'nuruodo (Thrawn), and it's not that much of a stretch. For more accuracy he would lead
Empire of the Hand instead.
Hutt Empire
Leaders: Jabba the Hutt
UU:
Jabba Desilijic Tiure
UU: Gamorrean, Nikto, or Klatooinian slave troopers perhaps
Black Sun Crime Syndicate
UU:
StarViper? Can't think of anything better. Swoop gangs maybe?
New Republic
Leaders: Borsk
UU:
Yes, beside Borsk Fey'lya, Leia Organa Solo is the only real possibility for Chief of State.
Vuuzhan Vong
Leaders: Shmrra Jaamane
UU:
Supreme Overlord Shimrra Jamaane, yes. Can't think of anyone else.
Possible new ones:
Xim's Empire
Leader:
Xim the Despot
UU:
War-Robot
Originally he lived at 1000 BBY, but he was retconned to 25K BBY.
Corporate Sector Authority
Leader: Should be ExO, but don't know any, so
Viceprex Hirken or
Fiolla if you stretch it a bit. Maybe
Odumin, heh.
UU: No idea,
Espos are only thing I can think of. Could be good at being garrison troops.
Ones I have suggested before for completeness:
Zsinj's Empire
Leader: Warlord Zsinj
UU:
Raptor commando
Hapes Consortium
Leader:
Ta'a Chume (and possibly
Tenel Ka Chume Ta' Djo
UU:
Hapan Battle Dragon
Galactic Alliance
Leader: Cal Omas
UU:
YVH droid
Corellians
Leader: Thrackan Sal-Solo
UU: Any ship by Corellian Engineering Corporation