I'm going to add to this over time, as it's a bit much to do all at once.

Old Republic
Bastila Shan, Jedi Master - I don't always enjoy playing against her, but she's what's made them good.
Old Republic Senator - Great CE, on a diplomat
Carth Onasi, Old Republic Soldier - I like his potential to unload massive damage on a piece then die. It's more fun than the GMA shoot then hide pieces.
Master Vandar - I'm not sure if he cuts it competitively, but he's a personal favourite.
Mirialan Jedi Knight - Acrobatic plus twin is fun, nice to see a usable low cost Jedi

Sith
Sith Recruit - it seems hard to think of creative ideas for scrubs - these are useful and fit the flavour of Sith really well.
Darth Revan, Sith Lord - the big movement piece
Darth Caedus, Sith Lord - the tough to kill piece - hopefully he'll be the basis for some competitive Sith squads that don't involve Revan, as previously it was hard to go past Revan.
Sith Blademaster - probably not the competitive option, but fun to swarm.
Exar Kun, Dark Force Spirit - fun force spirit, with some nasty Sith tricks.

Mandalorians
Kelborn - so strong for 28 points, that he seems like an auto-include - even without the amazing movement breaker he's still well worth 28 points.
Mandalore the Vindicated - beefy disruptive, good attacker.
Mandalorian Scientist - twin that can't be Bastila'd, and that's slightly more robust than the Czerka.
Fenn Shysa - arguably the best bodyguard in the game, with Beskar'gam, 90HP, and the ability to reprise attacks.
Mandalorian Tactician - great CE, might come into his own now the Mandos can make almost fully Cloaked squads.

Republic
Mace Windu, Legacy of the Light Side - fun beatstick.
Captain Panaka of Theed - makes Naboo Pilots brutal.
Naboo Pilot - really fun to play, not fun to play against.
Wookiee Jedi - all attack and no defence!
Anakin Skywalker, the Chosen One - mid-range beat stick with some fun options.

Separatist
Darth Maul, Sith Infiltrator - Sith Rage 2 is brutal, I enjoyed taking out a 160 HP Exar Kun in one activation.
General Grievous, Hero of Hypori - tough beatstick, Spinning Blade Attack rules.
BX Commando Droid Sniper - stealth, accurate, and 30 base damage? Brutal.
BX Commando Droid Spotter - Energy Shield is so helpful for the least mobile faction.
Aurra Sing, Assassin - her and Hondo look like a fun combination.

Rebel
Princess Leia, Rebel Commando - she can turn into a nasty secondary threat with some support.
Jan Ors - cheap shooter with potential to be boosted.
SpecForce Technician - hands out twin and jolt with Stealth.
Red Squadron Ace - great with Charging Fire and...
Jon "Dutch" Vander - nice Pilot booster.

Imperial
Darth Vader, Agent of Evil - super fun reserves piece.
General Weir - brings Storm Commandos back into serious contention.
Admiral Gilad Pellaeon - cheap Ysalamari, essential in many Imperial builds.
Nightsister Mother - lots of force lightning
Imperial Knight Strike Team Leader - I'm struggling for a second Imperial non-unique, but I imagine this makes Imperial Knights into an OK tier 2 squad?

New Republic
Galactic Alliance Special Guard - by far the best shooter non-unique the New Republic have IMO. Fragile, but lots of potential damage.
Gray Jedi - lots of potential damage output.
R2-D2 and C-3PO, Galactic Heroes - really useful utility piece.
Luke Skywalker, Galactic Hero - GMA is such a great CE for the New Republic.
Corran Horn, Jedi Master - Jedi Reflexes plus Opportunist is nasty.

Vong
Chazrach - love these little guys!
Nei Rin
Mezhan Kwaad - two great new Shaper options
Yammosk War Coordinator - stealing a Commander Effect is a fun idea
Yuuzhan Vong Hunter on Quednak - some scrub control

New Republic
IG-88A - gives a pair of shooters that have lots of different faction options
Celeste Morne - Sith Alchemy is a cool force power
Momaw Nadon - such a good idea for Mouse Droid control
Klatooinian Captain - well designed Pilot boost
Klatooinian Assassin - really good grunt who fits into lots of different factions

Man 3 Uniques is hard...especially for Sith and NR. But since this is favorite and not necessarily best that makes it a little easier....but only a little! I didn't just spend an hour on this before bed...ok I did.

OLD REPUBLIC
The Revanchist-Awesome figure with a fun CE. All in.
Atton "Jaq" Rand-Amazingly great shooter and door control
The Jedi Exile, Hero of Onderon-Such an incredibly interesting new take on the Exile and pieces. Her CE is so cool and new.
Mirialan Jedi Knight-I'm excited to try her out with a few different things. Being a non-unique force user with Twin and Acrobat opens some interesting options.
OR Senator-Fun for giving your favorite attacker an extra try! Always one of my favorite CEs

SITH
Darth Caedus, Sith Lord-My 3 favorite Sith Lords make the list! the WotC Caedus just wasn't all that great, this one captures his flavor perfectly and is a fantastic piece.
Darth Nihilus, Lord of Hunger-see above.
Darth Revan, Sith Lord-see above
Sith Recruit-Just perfection. Represents the expendability and usefulness and legions of people who are willing to give in the Dark Side
Elite Gunner-I really really like this guy, he is exactly what the OR and the Sith needed, a solid very boostable mid-cost Trooper

MANDOS
Mandalore the Vindicated-a Deadly shooter and an awesome CE
Gunsmith-Nice door control and a good shooter? you betcha
Mandalorian Protector-Goes great with my next choice
Fenn Shysa-I love his CE. Bodyguards get to return fire? Perfect
Jaina Solo, Sword of the Jedi (I'm going to cheat and put her here because NR is tight for me.) Jaina is one of my favorite characters and this version is just so good.

REPUBLIC
Republic Commando Atin-I had a hard time picking which of the new Commandos I liked the most...but I can usually find a way to run Atin
Null ARC Trooper Captain Ordo-I love ARC Troopers and this makes them so deadly and fun
Chief Tarfful-My Wookiee squad is maybe my favorite ever so more tricks for them=great and this guy is going to be a blast.
Wookiee Jedi-There is nothing not cool about a Wookiee with a lightsaber.
Spaarti Clone Demolitionist-Awesome cheap Clone Fodder

SEPS
Sev'rance Tann- I like Chiss, so I think a Chiss Dark Jedi is cool, plus makes my B3s better? All in.
Darth Maul, Sith Infiltrator-This is a nearly perfect Maul to me.
BX Commando Droid Sniper-a great Droid shooter who fits so well with IG-88 as well
BX Commando Droid Spotter-A great droid protector who helps the above shooter.
B2 Super Battle Droid-I just like Super Battle Droids...

REBELS
Master Yoda: Really fun with single shot or attack folks (Han Solos with FPs become very interesting) opens up so many posibilites of left out folks
Han Solo, Rebel General/Leia, Rebel Commando. I'm cheating. I adore the Versatility SA. Adore it. I had to put both here because they are so much fun.
Jan Ors-I'm cheating again. I actually prefer Jan in the NR where she really helps vanilla Kyle...I'm just so happy we got a Jan!
SpecForce Technician-A simply brilliant Support piece
Red Squadron Ace-Aces make up a very scary, and fun to play squad.

IMPERIALS:
Darth Vader, Agent of Evil- I love how this Vader Plays. A dangerous commander who comes in after the Troopers blow open the door and takes out the scary people still standing.
Desann-Finally! Desann, the awesome Dark Jedi Dino who fights Kyle Katarn and he does exactly what I wanted him to, fight hard, great Reborn CE, nice suite of evil FP.
Roan Fel-Love the Rivalry, love the Imperial Knight Boost, gives his daughter exactly what she needs, nearly perfect.
Imperial Knight Strike Leader-Give Imperial Knights some ranged D, exactly what they needed.
Reborn Shadowtrooper-A Really cool melee piece who goes great with Desann

NEW REPUBLIC:
So...difficult...brain....freezing...
Luke Skywalker, Galactic Hero: Perfect execution of Luke. Love him on so many levels. Exactly what the NR needed. Plus I love Luke Skywalker
Jacen Solo, Jedi Knight-Jacen's second appearance on this list. I put Jacen on any NR squad I can, and sometimes even when he won't always fit right. I just really like him, the piece and character
R2-D2 and C-3PO, Galactic Heroes-So much fun stuff to be had! Disruptive Bodyguards who hand out twin and relay orders? Simply perfect
Jedi Training Droid- droids with Saba's stats? Nuff said.
Galactic Alliance Special Guard-Can be so dangerous and are a fantastic trooper shooters for the NR, something they were in desperate need of.

VONG:
I don't really play Vong...ever...but I still have 1 favorite piece who I also cram into every squad
Vergere-doesn't hurt that Lily_Wan just made a great custom for me. I love giving folks crab armor and then throwin Verger to the Wolves to give a scary Jedi 4 more FP and MOTF+1

Fringe:
IG-88A- just pure deadly fun to play so many IG-88s!
Mara Jade, Smuggler- I find myself constantly thinking of new fun ways to use Mara
HK-47, Assassin Droid- An awesome disruptive meatbag killer with a great CE for droids.
Klatooinian Captain-Opened all kinds of fun Pilot shenanigans! I love the V-sets have made Pilot something worth having
Baran Do Sage-YOU TAKE IT BACK. WHATEVER YOU JUST SHOT AT ME. I love using him with Luke, Master of the Order. Oh it hit actually hit Luke past his crazy defense and the barrier? Ah the Sage will just take it.