Cannon Aiming: Spanish vs English and Chinese vs English?

Before the Armada fiasco. Spanish naval doctrine emphasized boarding enemy ships, rather than sinking them by gunfire, hence the tendency to aim for sails or masts, to reduce the mobility of enemy ships.

And yes, Chinese gunners did fire high during the Boxer Rebellion to attack the "spirits" of the enemy. This was not a regular military force, but a bunch of "fundamentalist" quasi-religious martial arts fanatics.

Just to expand on the concept of aiming at the sails and masts, as noted in another answer, this had to do with reducing (or even removing) the mobility of the target vessel. This applied right up to the end of the Age of Sail. With a cannon-armed sailing warship, the main batteries were aimed to the sides. There were generally only a handful of guns aimed fore and aft. In addition, due to the way the ships were constructed the bow and stern were structurally the weakest parts of the ship.

Therefore, if you were able to position your ship across the bow or stern of your target, you were able to fire all of your broadside cannon along the length of the target ship (known as raking) with the target ship having little way of returning fire. Naturally, the target ship would normally maneuver (as the wind allowed) to avoid getting into this position. If you shoot away the ship's masts, sails and rigging, the ship's ability to maneuver is reduced or removed completely. As with boxers, even a small advantage in agility can be enough to deliver a decisive blow.

In the event that a ship was immobilised or suffered significant damage to the sails and masts, it was not uncommon for the damaged vessel to strike its colors (surrender), even before an attempt at boarding was made, since it was at such a disadvantage in the battle. An added advantage was that the hull of the vessel was far less damaged with this approach, and the captured ship could be quickly repaired (ships generally carried spare masts, sails and rigging) and taken as a prize.

In the case of the English, they concentrated on reducing the ship's ability to fight back. Therefore they concentrated fire into the hulls of the enemy ships. This directly reduced the target ship's ability to return fire by killng the ship's gun crews, dismounting the guns and putting holes in the hull that let in water (men would be taken from the gun crews to man the pumps and assist with repairs).

However, this doesn't mean that the English (and later British) weren't also attacking the ship's sailing ability. The ship's masts passed through the hull to the keel, so shots into the hull below the masts could also bring down the mast. In addition, the ship's rigging was secured to the ship by chain stays mounted to the outside of the hulls. These were also vulnerable to shots aimed at the hull. Shooting away this rigging could also bring down the masts.

Finally, while it's generally accepted that the Spanish (and French) aimed high and the English aimed low, there are plenty of examples were individual captains did the opposite based on the circumstances that they faced. For example, if the target ship was right alongside, aiming into the rigging was impractical if not impossible.

As noted in the comments, as the years passed, a variety of different types of shot were brought into use. Of course, the general purpose round shot was always an option - a direct hit could fell a mast, carry away a sail, shatter a rigging block or chain stay. Then there were the 'shotgun' options of grapeshot and langridge (odd bits of iron and nails), which could shred sails, cut ropes, etc.

The more specialist types included chain- and bar-shot, these used chain or a solid metal bar to link to cannon balls (or, in some cases, hemispheres). These improved the chances of hit on rigging, masts and spars, and could prove very effective at short range. Finally, towards the end of the Age of Sail, a wide variety of 'dismantling shot' designs appeared, such as star shot (favoured by the early US Navy). These were variations on chain and bar shot designs, which opened up on leaving the barrel, again with the aim of increasing the chance of catching a part of the rigging.

In all cases, the dismasting shot had a reduced range compared with round shot and was even less predictable in terms of flight path. While it could be used in an anti-personnel role (again at short range), it was far less effective against the hull of the vessel, in comparison with round shot.

Sources:
Fighting at Sea in the Eighteenth Century, the Art of Sailing Warefare, S. Willis (Boydell, 2008)
Naval Warfare in the Age of Sail, The Evolution of Fighting Tactics, 1650-1815, Tunstall/Tracy (Conway, 1990)
Frigates of the Napoleonic Wars, R.Gardiner (Chatham, 2000)