I hear a lot of talk about what is and isn't "piracy" in EVE-Online. As far as I'm concerned, piracy is whatever we mean by it; it could be something different for you than it is for me. But in this post I thought I would catalog the acts that fit my definition of piracy.
Highsec piracy falls into three categories: those crimes that rely on the target to flag himself a legal target, those crimes that incur the inevitable wrath of CONCORD, and war.
Can-flipping targets highsec miners who, to save time, routinely transfer ore from their cargo holds to a jettisoned cargo container. Such containers, known as "jetcans," have a much higher capacity than most miners' cargo holds. Once the jetcan is full, the miner warps to a space station, leaves behind his mining ship, and returns to the jetcan with an industrial ship to retrieve the ore. The pirate steals the targets ore and leaves it there in a jetcan of his own. The newly-emptied jetcan disintegrates with nothing inside, leaving the newly-filled jetcan instead. The new can will appear yellow, rather than white, to the miner, and the pirate will begin flashing red on the miner's overview display; these clues indicate that the can or ore does not belong to the miner, and that the pirate is a legal target--he has been flagged so for 15 minutes for stealing the miner's ore.
At this point the pirate is at risk; he can be attacked, but he may not legally engage first. Most pirates aren't bothered; they came to the party in a PvP-fit ship, while the miner is encumbered with such modules as mining lasers, strip miners, and mining drones. Any such miner who is fool enough to defend his ore under such circumstances is quickly spanked. What many novice miners don't realize, however, is that taking the ore back makes them legal targets for the pirate--in effect, they have stolen the ore (back). If the miner reclaims his ore, whether in ignorance or under the sad assumption that the pirate has moved on, the pirate quickly takes advantage of his kill rights.
To avoid being victimized by can-flipping pirates, miners may (1) simply choose not to mine into a jettisoned cargo container, (2) gracefully admit their mistake when the ore is stolen and consider the ore lost for all time, or (3) exchange their mining vessel for an uber solo pwnmobile or equivalent gang of mates before engaging the pirate or reclaiming the ore. As an alternative to jetcan mining, I suggest anchoring a large secure cargo container at the mining point instead. Pirate's can't so easily steal ore from password-protected containers.
Wreck-baiting, like can-flipping, depends on the target taking some positive action which renders him in the eyes of CONCORD a legal target for the pirate. In this case, the pirate prowls a system's (or a few systems') asteroid belts and ice fields, killing rats but being careful to leave loot in the wrecks. Any player who comes across those wrecks and takes the loot for himself is flagged for 15 minutes a legal target for stealing loot which legally belongs to the pirate. You may be sure the pirate is not far away, looking above all for pilots who are flashing red on his overview...and when he finds you, chances are you'll be sorry. Such pirates sometimes give themselves away by swooping in on another ship in the vicinity of their wrecks; when they see that their loot has not been violated, they rather lamely move along...but remain close enough to take action should it become possible.
Suicide ganking refers acts of sheer agression that doom the pirate to swift retribution at the hands of CONCORD. While such pirates may be crazy, it's more likely that they are well-informed and well-organized. Suicide gankers consider the cost of their ship and fittings against the proft to be gained from looting your wreck. They have likely scanned your cargo, so they don't sacrifice themselves for a cargo of dolls or janitors; instead they're looking out for original blueprints or high-end fittings or rigs and the like. They also tend to work in teams, so that even while the ganker is fleeing in his pod, his confederate is scooping up the surviving cargo from both wrecks.
War deccing (piracy by declaration of war) is an organized form of extortion. Some pirate corporations specialize in disrupting the lawful activities of industrial corporations to the point that it is cheaper for the target corp to pay a ransom than to wage war. Such pirates like to target small- to medium-sized corporations with PvP capabilities that are comfortably within the pirate corp's ability to face. Simply by declaring war on a target corporation, that corporation's pilots all become legal targets as far as CONCORD, sentry guns, and faction police are concerned. As with most other pirates, war-deccers tend to enjoy combat about as much as profit, and are not at all sorry when their targets decide to fight rather than pay. Still, they are professionals, and in the end they usually get paid.
Mercenaries also rely on declarations of war to gain legal aggression rights against corporations, but rather than earning money primarily through extortion, they work on a contract basis for third parties. Being targeted by a war-deccing pirate corp? Being elbowed out of the belts by a rude industrial corp? A mercenary corp will be happy to come and augment or replace your own corps' more limited PvP capabilities--for a small fee, of course.
In highsec space, if you keep your nose clean--if you don't loot other people's ships, if you don't take ore from other people's cans (not even if they're right where yours used to be, and have the same name), and if you don't shoot first at other people's ships, chances are you'll be free of problem pirates. But if you are known to be traveling with a hold full of expensive cargo, travel with care to avoid suicide-gankers; and if you catch the eye of a pirate corp bent on extortion, calculate what you'd pay for the right to continue your operations free of disruption.