To go greek is to be a willing recipient of anal sex; this phrase usually refers to the first time this occurs, but can be applied to a veteran too. The 'g' in greek can be capitalized, but it doesn't change the meaning. This slang originates on the US east coast, but hilarious misuse of it pops up at universities all over the country during fraternity and sorority rush weeks, since a lot of them make signs and banners saying 'go greek'.
My girlfriend finally decided to go greek.
Did you know that Josie goes greek?