These are most common,

AAMOF
as a matter of fact

ADN
any day now

AFAIA
as far as I'm aware

AFAIC
as far as I'm concerned

AFAIK
as far as I know

AFK
away from keyboard

ASAP
as soon as possible

ATSL
along the same line

AS
another subject

BAK
back at keyboard

BBD
basically brain dead

BBL
be back later

BCNU
be seeing you

bf boyfriend
BFN
bye for now

BRB
be right back (when momentarily leaving a chat )

BTT
back to topic (on email lists, message boards) back to top (to keep subject from ageing off a message board, a use rather frowned upon)

BTW
by the way

CU
see you (as in "CU 2morrow!")

CUL
see you later (or CUL8R)

DEB
don't even bother

DGT
don't go there

DH
dear heart (or husband)

DIIK
damned if I know

EM(F)BI
excuse me (for) butting in

EOM End of Message
FUBAR
fouled up beyond all recognition

FWIW
for what it's worth

FYATHYRIO
having to do with a self-directed, physically impossible action, and a horse

<g> grinning; grin. The comments preceeding or following <g> are meant humorously or to be taken with a grain of salt.
GD&R, <gdr>
grinning, ducking and running

gf girlfriend
GIWIST
gee, I wish I'd said that

GMTA
great minds think alike

HTH
hope this helps!

IC
I see

IIRC
if I recall correctly

ITSFWI
if the shoe fits, wear it

IMO
in my opinion

IMCO
in my considered opinion

IMHO
in my humble opinion

IMNSHO in my not so humble opinion
IOW
in other words

IRL
in real life (as opposed to your online life!)

jk just kidding
KHYF
know how you feel

L8r
later

LAB&TYD
life's a bitch & then you die

LTNT
long time, no type

LOL
laughing out loud

NBD
no big deal

NOYL
not on your life

NP, np
no problem

NTYMI
now that you mention it

OIC
oh, I see!

OOTQ
out of the question

OT
off topic

OTOH
on the other hand

OTTOMH
off the top of my head

PITA
pain in the nether regions

PTB (the) powers that be
POV
point of view

RABNC
read and acknowledged, but no comment

RSN
real soon now

RO(T)FL
rolling on (the) floor, laughing

ROFLMAO
rolling on floor, laughing my --- off

ROTFLOLSTC
rolling on the floor, laughing out loud - scared the cat!

RTFM
read the flippin' manual

SEP
someone else's problem

SNAFU
situation normal, all fouled up

STFU shut the **** up
SO
significant other

SOW
speaking of which

TANJ
there ain't no justice

TANSTASQ
there ain't no such thing as a stupid question

TCGOFE
this could go on for ever!

TEOTWAWKI
the end of the world as we know it

TFTHAOT
thanks for the help ahead of time

TIA
thanks in advance

TOBAL
there oughta be a law

TOBG
this oughta be good

TPTB
the powers that be

TTBOMK
to the best of my knowledge

TTFN
ta-ta for now!

TTUL
talk to you later

TYVM
thank you very much

WB
welcome back!

WRT
with regards to

WYSIWYG
what you see is what you get

WTG
way to go!

YGLT
you're gonna love this

YMMV
your mileage may vary (= your experience may differ)