Well, to start, most "ancient" states are not particularly analogous to modern states in terms of a criminal justice system. Even Rome (I cannot speak to the Hellenistic equivalents) maintained a significant degree of "family", or perhaps more properly, paterfamilial, justice even through the early to middle stages of the Empire (it's somewhat besides the question at hand, but the Roman legal system had a rather fascinating evolution, starting with Augustus' reforms, slowly leveraging state authority over areas that traditionally would have devolved to the paterfamilias level. The Digests and other jurist opinions are simply fascinating reads).

That said, one example that kind of springs to mind is Alcibiades. He's predominantly known now for his (minor) appearances in Socrates'/Plato's work, but he was a leading statesmen/politician/general during the period of the Pelopennesian war. He pulled off the rare feat of angering everyone, first the Athenians (who exiled him for sacrilege, which he may or may not have committed), then the Spartans, then the Athenians again, and finally the Persians. He wasn't so much a criminal as an opportunist (he is much more complicated than that, frankly, he's one of the most fascinating personalities of antiquity), but by the end of his life he was a reviled by pretty much all sides.

During Roman's time: Strabo in his "Geografia" talks about a sicilian brigand called Seleuro. He was a farmer and then started organising attacking cities with his gang. Then there is Lucusta, which is considered to be one of the first serial killers, her most famous victim is the Emperor Claudius, killed with poisoned mushrooms. Cassio Dio recalls a certain Protogenes (LIX-26), who was the "sword and the dagger" of Emperor Caligula, he was finally put to death by Emperor Claudius.

Then there was the constant problem of piracy and the several servile wars. I don't think that persons such as Teuta (Illyrian queen and pirate) or Spartacus (rebel slave) can be considered as criminals since they were enemy of the states and Rome had to deal with them on the field of battle.