Are chapter and verse divisions international? If someone quotes e.g. Leviticus 6:7, will this be the correct position no matter the language or translation?
In general, yes...
As Affable Geek answered, the divisions predate the printing press but were not part of the original texts.  There aren't that many publishers of Bibles and most of them use the same system that English translations have used since Langton.  So if you go to a Spanish-language service anywhere around the world, you can find your place in the text.  (Assuming you understand Spanish, of course.)
It seems likely that this is for convenience and because of the network effect.  Since most tools of interpretation (dictionaries, commentaries, concordances, etc.) use the standard system, most people who purchase a Bible will expect to find it to be compatible to that system.  A publisher would quickly go out of business if they tried to introduce a novel system.
with two exceptions.

The Tanakh
As H3br3wHamm3r81's answer notes that the Jewish Bible (what we call the Old Testament) uses a different system.  Since Judaism has a separate apparatus of interpretation, Jewish publishers divide chapters and verses in slightly different places.  It's not different enough to cause major problems, but we have experienced confusion over on Biblical Hermeneutics.  One noticeable pattern is that Psalms in Jewish translations often make the short descriptive text (ascription) part or all of verse 1 in contrast to Christian translations.  For this reason, I like to quote Bible passages or at least link to them rather than just include bare citations.

The Psalms
The earliest Greek translation of the Tanakh included a slightly different order of the Psalms then the Hebrew original.  Since the standard system adheres to the Hebrew order, this is normally not a problem.  But it's something to be aware of if you are talking Psalms across the Eastern/Western divide or if you are reading Catholic liturgy (which uses the Greek system for some reason).



As it turns out, Leviticus 6:7 is not the same between the Christian system and the Jewish system:

And the priest shall make atonement for him before the LORD, and he shall be forgiven for any of the things that one may do and thereby become guilty.”—Leviticus 6:7 (ESV)
And this is the law of the meal-offering: the sons of Aaron shall offer it before the LORD, in front of the altar.—Leviticus 6:7 (JPS)

It turns out the Jewish system puts what we call Leviticus 6:1-7 into the end of chapter 5 as verses 20 to 26.