Alright! I noticed an obvious exception from the list of threads here: no Kombos for the warriors! Let's post 'em....

p=b button (punch, even though it is button #1, it's usually a punch), k=a button (kick), u=up, t=towards, b=back, d=down....etc.

Johnny Cage
Karate: p,p,t+k,u+k (hint: duck and block right after, and, normally, the opponent will attack, then you can combo again.) k+k
Jeet Kune Do: t+p, t+p, k,k, t+p (I only recently found this because Karate's combos is so good, I'll need to try it out.)

Sektor
Ninjitsu: ?
Sambo: p,p,k

Scorpion (I know he has more, but I can't think right now....)
Hapkido: p,p,k
Pi Gua: p,p,k

Shang Tsung
Any: d,t+a, u,d+b, d,a+b (it's tricky, and can be changed around well.
Snake: a+p,p
Crane: ?

Bo'Rai Cho (he has quick recovery on his combos, so even if some of these listed aren't actual combos, they will usually work in Kombat.)
Drunken Fist: p,p,p p,p,k k,k,k (man, he's easy....)
Mi Zong: p,p,t+p (or just p over and over.....)

Quan Chi
Any: a,t+k, d,a+p
Tang Soo Do: t+p, a+p
Escrima: t+p, a+p

Raiden
Nan Chuan: p,p,k,d+k k,k,u+k (against wall)
Jujutsu: p,p,k,d+k

Sareena
Tae Kwon Do: p,k,d+k
Yuan Yang: k,t+k,d+k

Nitara
Leopard: p,p,k,d+k p,p,u+p
Fu Jow Pai: b,b,a (you can sometimes add a d+p or u+p after this, it depends on how the other player reacts.)

Mavado
Long Fist: p,p (can be finished with about any of his moves, but works best with t+k...he's slower than christmas and is relly open for interupts.)
Wing Chun: no really good ones....

Hsu Hao
Shuai Chiao: p,p,k, (a+k, sometimes...)
Wrestling: ?

Reptile
Hung Gar: p,k,t+k
Crab: p,t+k, t,d+k

Cyrax
Ninjitsu: p,p,k (add one of his special moves if against a wall.)
Sambo: p,p,k, (sometimes u+k)

Drahmin
Netherealm: a+p, t+p, d+k
Oni: ?

Noob Saibot
Hapkido: p,p,k
Pi Gua: p,p,k

I substituted p and k for b and a in here, at one point, then realized away was a, so I had to re-change it. If any combos don't work, that's probably the reason, or I just goofed.

My personal favorites are Johnny Cage and Scorpion, who can dominate an enitre match (even on very hard or against a good opponent) if you really know how to use them. On my profile it says my best is Cage.

Feel free to add to the list, guys.