If you somehow don't already know this (and if you don't, bookmark this site), OMG means "Oh my God" in textspeak (or 'txtspk', if you're cool enough...I'm not)
OMG is a recent addition to the Oxford English Dictionary (OED), and it's definitions are listed as follows:
Colloquial (frequently in the language of electronic communications)
A. interjection or noun
Expressing astonishment, excitement, embarrassment, etc.
Causing or characterized by a reaction of astonishment, excitement, etc.; that might cause one to exclaim 'oh my God!'
Most of the examples given in the OED are from the 1990's and 2000's, but the adjective form is actually attested in 1982 in reference to some (apparently) really good tangerines.
But the really interesting citation dates to...drum roll please...1917!
Memories, a book written by Baron John Arbuthnot Fisher Fisher and published in 1919 contains the first known usage of O.M.G. in print. He wrote:
"I hear that a new order of Knighthood is on the tapis - O.M.G. (Oh! My God!) - shower it on the Admiralty!"
Now, I don't think anyone is alleging that modern users (and over-users) of OMG were in any way influenced by a man who died in 1920...but it is safe to say that we didn't think of it first.
Shout out to The Virtual Linguist for mentioning this a few days ago.