I'd say that a lot of what has become organised crime groups grew out of older bandit and gang activity - it's just that they've become more organised and cooperative in modern times.

(Also, I am uncertain about whether to mention piracy here - it was organised to a certain degree, and they were certainly committing crime)

The Chinese triads and tongs go back quite a long way. According to popular myth, they have their origin in Ming-loyalists rebelling against the new Qing emperor post-1644, though how much of that is true is anyone's guess. A more accurate origin of what became modern triads/tongs is the Heaven and Earth Society (Tiandihui), which is first recorded in 1762. The Tiandihui grew and spread throughout China and the rest of the world, branching off into rival groups.

The Yakuza, too, claim older origins going back as far as the 18th century, to groups of itinerant gamblers and peddlers of stolen goods - though they also like to claim some sort of connection to the samurai, possibly as a way to legitimise themselves.

Some parts of the UK have a documented gang culture going back to the 1850s - Glasgow, for example. Many of them were so-called "penny mobs" - named such for the practise of being bailed out from jail at the cost of one penny per gang member. Penny mobs also existed in the US.

This info is drawn mainly from Organised Crime in History, by Mark Galeotti, which is unfortunately out of print. The Origins of the Tiandihui: The Chinese Triads in Legend and History might also be of interest.