What metaphor do countries that don't play baseball use for intercourse?
I'm from England and when I was in high school (so up to 4 years ago) it was common practice to use the same metaphor, and for the most part, everyone had a different definition of what each base stood for. Nobody really cared much for where the metaphor came from, then again, this could be due to it being a girls-only school.
Now, a lot of people in my environment refer to the act of first intercourse with a new person by saying they "scored", e.g.
Did you score with the chick from last night?
In general I still sometimes hear people referring to the whole "courting" process as "playing the game" which I suppose, carries the notion of escalating towards a "win", which you mention.
Baseball is rarely played here in Australia but everyone knows this analogy. First base is the first kiss and third base is just about to score. The home run is not much used however everyone would understand.
As for other metaphors. Get it on, do the wild thing, check the plumbing (in the right context), make the earth move, score, do her, knock her up (with pregnancy), make a woman out of her. The list goes on, descending into unsavory slang and sexism.
In Australian slang, the term Have a bat... can mean to masturbate relating to sports from Cricket and of course to Score is to have sex - although I am unsure what sport in particular that refers to, I am assuming it is simply a generalisation.
Speaker hasn't specified whether she wants to limit the scope of countries to the English speaking ones or not.
Anyway, I am from Pakistan and over here there are a lot of different metaphors and idioms that are in use. Please note that I am translating from Urdu to English, the metaphors are used in Urdu.
Night match Cricket is pretty common here, and night matches of cricket is something the youngsters look forward to.
Play usually, we get the true meaning of the verb by the context. So if a person says playing with one wife is a widespread past time, we know that she means.
Another verb which is used, usually in slang or derogatory terms is thokna. Thokna is an Urdu word which basically means to beat something with something else, like driving a nail into wood or wall with a hammer. These two could be the two most widespread uses of this word. It is considered very rude to use this for sexual activity.