Here's what I heard from Rabbi Yitzchak Breitowitz on the subject:
The Aruch HaShulchan (living in Russia a hundred years ago) wrote that if a government's laws are fair to everyone, "like England's laws, or the Glorious Czar's", then no prohibition of mesira ("snitching") applies.
Some feel that the entire sentence was written to placate the censor, and none of it is accurate.
Rabbi Breitowitz, however, felt that what happened was, Rabbi Epstein first truthfully wrote the following halacha:
If a country's laws are fair to everyone, like those of England, then no prohibition of mesira applies.
He then realized what would happen to him if he implied that the Glorious Czar's laws weren't so wonderful, so he added in "or the Glorious Czar."
Rabbi Breitowitz then stated that some poskim (Rav Wozner, if I recall) go further and say that any time halacha recognizes the state's laws (dina d'malchusa dina), then there is no prohibition of mesira to help the government enforce those laws.
Rabbi Hershel Schachter is known for pointing to a Gemara of a rabbi who would point the Roman authorities to circumstantial evidence that a Jew was a thief, for which the Romans could give the death penalty. Eliyahu HaNavi told the rabbi this was no job for a nice Jewish boy and distasteful, but not that it was prohibited.
Q: "But wouldn't the owner [i.e. G-d] of the vineyard [the Jews] prefer there be no weeds [thieves] in it?"
A: "You let the vineyard's owner sort that out for Himself!"
Lastly, if the punishment given by the authorities would be no worse than what halacha would require (and a halachic court would have no way to enforce their decision), then it also wouldn't be a problem. In the case of a Jew who was caught stealing Torah ornaments and it's up to the synagogue to decide whether to press charges, Rav Moshe noted that halacha would require a monetary fine but no jail time; if pressing charges would send this fellow to jail (a potentially hellish experience), he recommended against it.
Traditionally there were also cases where a fellow's crime (e.g. counterfeiting) would reflect badly on the entire Jewish community and lead to more persecution; I don't know how/if that would apply today.