I've gone through this a number of times in a persistent role as someone from the "Democratic People's Republic of Korea" (the official name of North Korea).
Not the "oh god get me out of here" kind, the "this greatest nation in world" kinda.

Connecting to server...
You're now chatting with a random stranger. Say hi!
Stranger: hi
You: herro
You: you should come to korea
You: is great nation
Stranger: north or south korea
Stranger: ?
You: Democratic People's Republic of Korea
You: under glorious leader
You: nation is best of world
Stranger: my grandpa is war veteran of korea
You: he come too
You: we have special place for him
Stranger: ok we too
Your conversational partner has disconnected.

Hi there PID666 XD
I lol'd

I got a couple of funny'ish omegle ones today, but nothing truly noteworthy

EDIT:
Connecting to server...

You're now chatting with a random stranger. Say hi!

You: hi

Stranger: Oi! You there!

You: Oh noes

You: It's da FUZZ!

Stranger: haha

You: RUN!

Stranger: RUN AWAU!

Stranger: *AWAY]

You: Gah, Help!

You: Damn

You: FFFFFFFFFFFFFFFFFFFFFF-

Stranger: omg its sooo not as affective with a typo haha :L

You: I shoulda had a v8!

Stranger: haha!

You: Damn, where's the V*8?

You: My car's only a v4 D:

You: damn

You: FFFFFFF-

Stranger: i dont drive!!

Stranger: OH NO!

You: OSHIT, it's USAIN BOLT!

Stranger: a WHAT!?

You: FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFF-

You have disconnected.

Stranger:  WELCOME

  You: TO

  Stranger: I have some  interesting things for sale stranger

  You:  WOOWOWOWOWOWOWOWOW!

  You: Like a FEMALE?

  You: I WANT  FLESHLIGHT!

  Stranger: What are you  buying

  You:  OMGOMGOMGOGMOGMOSMODGIJOQIJW"OIJSGSDKFJ: IJF:IJW:EUHF:IU SHV:S

  You: DILDOSWORD NOW!

  Stranger: what are you  selling

  You: My PENIS

  You: RAWR

  Stranger: Ahhh I'll buy it a  highj price

  You: Suck it first

  You: You gotta bite it  off

  Stranger: come back any  time

  You: BITE IT OFF  DAMMIT!

  Stranger: I'm an australian  guy bitch

  You: SO?

  You: BITE IT OFF

  Stranger: grabs  chainsaw

  You: So I can sell it to  you

  You: SHIT

  Stranger:  ahhhhhhhhh!!!!!

  You: *Goes super  sayn*

  You: KAMEHAMEHA!!!!!!

  Stranger: turns super sayn  level2

  Stranger:  KAME


  You: I'm a chargin mah  lazer!

  Stranger:  KAAAAMEEEE

  You: FFFFFFF

  Stranger:  HAAAAHHHHHHHHH"!!!!


  You: SHOOP SHOOOP  SHOOOOOP!

  Stranger: *_*

  You:  WHOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOP

  Stranger:  AHHHHHHHHHHHHHHHHHHHHHHHHHH!

  You: I'ma firin mah  lazer!

  Stranger: your attacks are  weak 

  You:  WHOSIDFHOWHEFIHASPBJFIYALSF!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

  Stranger: just like your  father

  You: You are weaker than my limp  penor

  Stranger: timeback  slash

  You: NOOOOOOO

  Stranger:  *shikaw

  You: *Erection  meltdown*

  Stranger: *anime music in  the background*

  Stranger: FAAALCON  PUNCH

  You: I summon Whoreslutshield of  orgasmic doom!

  Stranger:  huuh!!!??

  You: She was  dispensible

  Stranger: GIAAAAAAaA  nasaada.....

  Stranger:  nasadaaaaaaaaaaaaa!!!!!!!!.....

  You: OSHIT,

  Stranger: *dies*

  You: Attack of  dyslexia

  Stranger: X_X

  You: gurgle of death

  You: *inserts limp dick into dead  mouth*

  You: hhehe

  Stranger: mom is that  you

  Stranger: NO!

  Stranger: shit

  You: Lols

  You: MAKE YOUR MOM SUCK IT  TOO!

  Stranger: I will  never

  You: Oh suck the  limpness!

  Stranger: jumps to building  

  You: Too bad you're  dead.

  You: *he falls to the ground,  dead*

  Stranger: o shit I  forgot

  You: OSHIT, how are you  speaking?!

  You: *Inserts dick  harder*

  Stranger: I'm dead so  bye

  Your conversational partner has disconnected.

Lol, merchant from Resident Evil.

Connecting to server...
You're now chatting with a random stranger. Say hi!
A word of advice: "asl" is boring. Please find something more interesting to talk about!

Stranger: hey its getting to be that time of night for me and im looking for a girl who will talk dirty to me and it would be sweet if they had a webcam :D if not sorry to bother you
You: Sure, but I would prefer your address so I can come over there and beat you to death with your own severed arms before pissing on your lifeless corpse.
Stranger: :(
Your conversational partner has disconnected.

Just a quickie.

Better then sex.

Pwnt.


Gj.

Ha! They started with word advices.

"A word of advice: "asl" is boring. Please find something more interesting to talk about!"

Double post:

Stranger: Hello!
You: Good day.
Stranger: How is life
You: Its going on.
You: Im afraid to die everyday
You: My wife just left me.
Stranger: Sucks man.
Stranger: So, you're going to get pissdrunk
Stranger: and drink away all your problems?
You: Apparently.
You: But who needs a wife when you have rape.
Stranger: hmmm
Stranger: That reminds me of my dad.. he always used to say that
Stranger: *wipes away a tear*
You: Maybe your my son...
Stranger: Nah
Stranger: I hope not
Stranger: ^^
You: I HATE YOU :Д(
You have disconnected.
-----------------------------
Stranger: hi
You: hi
Stranger: from
You: earth
Stranger: me too
You: no shit sherlock
Your conversational partner has disconnected.

shins was LOLtacular :]

Nice ones dash.
I'm tired of asl myself