The simplest answer: Flintlock musket, flintlock pistols, flintlock blunderbusses, swords of various kinds (that varied from the "hangar" to the "cutlass" and rarely the rapier), boarding ax, boarding pike, and any other material that could be used as a blunt instrument if one ran out of weapons previously listed. On top of that, we could add onto that we could add hand held explosives like granadoes (grenades, basically a iron sphere with powder in it, and sometimes not even iron) and stink pots. I assume we aren't talking about artillery on ships in this question.

Longer answer: In general, a firearm was preferred over a bladed weapon by pirates (and any sailor for that matter) since using a firearm meant you might take out your target without having to come close to them and possibly exposing yourself to their attack. It was also an ideal way to target crew over ship (which may be part of what the pirates wanted to take, and artillery fire could also damage cargo which the pirates wanted, and muskets used less powder). A sword, while it doesn't require ammunition to use to it's full potential, required skill to use if one wanted any decent effect, so while you may get the pirate who happened to be on a privateer or Navy ship that got fortunate enough to be in several boarding engagements that required close combat and got first hand experience using the cutlass, most men had no prior training in using the sword. There was much more likely a chance of a man having gone to a festival on land and witnessing/participating in a cudgel combat contest than actually getting training to use a sword at sea outside of combat (though it happened at least a couple of times, but it doesn't appear common, the training may have used cudgels to help with he training, and there weren't any formal schools or methodologies of naval close combat at the time). The already basic cutlass (with it's large amount of steel behind the blade that didn't even need to be that sharp to do horrible damage) was pretty much like a iron rod with a handle in the hands of a inexperienced men. Unfortunately, Hollywood has taken the greater public for such a ride with it's grandiose images of large masses of men almost exclusively armed with incorrect cutlasses for the period fighting over conveniently large decks - that it's hard to dissuade the public from being convinced otherwise. Along with this image, people also have issues getting beyond every boarding being done by pulling alongside the enemy ship and having the whole crew boarding. Sending a whole crew wasn't necessary all the time (and might be inconvenient) and plenty of boardings took place by boat while the pirate ship covered the boat's boarding. You don't have to send 100 men over to take out a crew of 10 every time, you send what is necessary (and what you're willing to risk).

The firearm on the other hand, not much skill or time needed to train a man to point and pull a trigger (plus the other advantages mentioned previously). The pistol was best used in extremely close combat, since the deck is moving below you and pistols at the time had smoothbore barrels (no rifling in the barrel to give the ball a spin so it could fly straighter), it's not impossible for the pistol to miss even when you are relatively close to your target (making the action of putting the barrel of the pistol straight into the gut of your opponent and pulling the trigger the best way to guarantee results). This is why pirates who boarded vessels often opted for carrying multiple pistols (and even muskets). Multiples also helped combat a really big disadvantage of flintlock firearms - misfires (could be bad powder, wet powder, flint used up, flint broke, flint went missing, the frizzen (or steel as they called it back then) needs to be replaced or treated to help it spark again, the mainspring is finally worn out, something fowled the lock overall, the barrel and/or touchhole needs to be cleaned out, and who knows what other problems could contribute to a misfire).

Basic strategy to remember with pirates, weapons, and tactics - pirates are criminals, not necessarily warriors fighting for a cause, but men fighting for themselves and profit. It isn't profitable to risk powder and men in battle if it can be avoided. That's why a pirate's best friend (and most often used friend) was surprise and demonstration of overwhelming force to either convince an enemy to surrender or to hopefully subdue the enemy before they can offer a serious counterattack. This is why, many more times than not, pirates opted to avoid Navy vessels and lost horribly to Navy vessels in combat (since Navy vessels were actually prepared to take on the pirates and had the weaponry to do so) - taking on Navy vessels, while some pirates may have been able to pull it off, also mean high risk of death (so if taking on the Navy, the reward better be worth it).

Highly recommended source in concerns to this topic: Benerson Little's The Sea Rover's Practice, the only book of notable size and merit to concentrate on piracy and their tactics. He has a whole chapter on just the weapons.