Outside of the resurgence of ramming which came along with the development of armored ships, arguably beginning with the ramming of the Cumberland at the Battle of Hampton Roads in 1862, and continued throughout the riverine campaigns of the American Civil War before being picked up by foreign navies (see the Battle of Lissa (1866) and the Battle of Iquique (1879) there is very little mention of ramming as anything but a last-ditch tactic.
In my opinion, the more interesting thing about this question is why ramming fell out of favor. Why does the battle-tried bread-and-butter tactic of great navies from at least 535 BC until the Dark Ages1 simply vanish from use following the Battle of Lepanto in 1571 (the last instance of galley warfare as we generally think of it) and remain more or less completely unused for the next 300 years?
To understand this, we need to look at the differences between galley warfare and the naval warfare of the Age of Sail. Galley warfare is what might be termed “consolidated” warfare- it almost always occurs between large fleets and has as its goal the destruction of the enemy fleet. In a fleet engagement such as this, there is a great deal more support available than in a smaller engagement, so the risk of accidental death due to ramming (i.e. sinking one’s own ship by ramming another) is perceptually reduced. The battles during this time also take place in fairly calm seas with which the participants are familiar; this also makes ramming ‘safer’ from a psychological perspective. From a technological perspective, there is no really effective anti-ship weaponry available (even ballistae are incredibly difficult to fire accurately at a moving target while pitching and rolling in the sea) at the time, so ramming has de facto standing as the most effective anti-ship tactic simply because it is pretty much the only anti-ship tactic.
Warfare in the Age of Sail is much different, it is primarily “distributed” warfare. Mostly small engagements over a wide area in all weathers, with various goals. Prize money becomes an increasingly important factor in this era, so the goal of engagements becomes less about destroying the enemy fleet en masse and more about capturing the individual ships that made up the enemy fleet in small chunks, to increase the size of one’s navy and inflate one’s pockets. In a tactical climate like this, ramming carries a very low cost-benefit. For one thing, ships in the Age of Sail were designed to carry lots and lots of guns, not a ram; this being the case, ramming is far more dangerous to both ships than it would have been in the days of galley warfare. If you ram someone and either ship sinks, you’ve lost out on a lot of potential prize money. The fact that battles often took place in varied locales and weathers also contributed to the deprecation of ramming, as sailing ships are bound to the wind whereas oared vessels are not. There exist a great many battle scenarios where actually positioning in such a way as to be able to ram the enemy would be more or less impossible- in these situations, guns provide an advantage, because they increase the area in which you are able to fight your enemy. Instead of having to be right up against them, you can be right behind them and chasing them while fighting. The increased use of guns also made ramming less desirable in that even in ideal ramming conditions, ramming would require you to run straight into the enemy’s fire, risking heavy damage to your ship and crew. Worse, at the end of the day, if you decided to pull alongside in the same conditions and exchange point-blank broadsides with the enemy instead of ramming, you’d probably do more damage than you would if you rammed them.
One other reason that navies in the Age of Sail did not ram might have to do with the development of European naval warfare. For a large portion of history, European navies fought naval battles by tying their ships together and fighting what amounted to a land battle at sea (see the Battle of Svolder (1000) and the Battle of Sluys (1340)). Because of this, tactics developed in a much different way in the European naval tradtition than the Medeterranean/Arabic tradition (i.e. the fo’c’sle or forecastle was basically an attempt to copy the effectiveness of a fortress on land for application at sea during battles of the lash-the-ships-together-and-thunderdome-it-out type, and ships themselves grew out of this to be mobile, long range fortresses capable of supporting populations (almost like little towns) rather than purely offensive weapons like galleys, which were short range, crewed by comparably few men, and pretty much disposable).
The reason you see the move back to ramming with the onset of the Civil War is because the tactical climate shifts back to “consolidated” warfare of a slightly different kind. In this case, combat doesn’t occur between large fleets because ironclads can just annihilate any wooden ship you throw at them- instead, it occurs between high value targets- the most important ships in the fleet. Just as in the days of galley warfare, you have the factors of localized combat, predictable weather/seas, and the ultimate goal of destroying the enemy’s ships- what is really interesting, though, is that once again we see that there is no effective anti-ship weapon. Ironclads are highly effective against wooden ships, but they can’t do anything to one another ( for the most part the cannonballs just bounce off the armor), and since this is the case, ramming once again becomes a viable tactic. Since being chewed up by the enemy’s guns on approach isn’t an issue anymore because of armor, and since due to the advent of steam wind position and current are trivial aspects of a typical engagement (i.e. captains no longer needed to wait for the wind to shift just right to be able to get into ramming position), it makes sense to start ramming once more, as it is a means of attack capable of piercing through armor and achieving the desired end result of destroying the enemy.