As elsewhere in the medieval era (and later eras) it depended entirely on the social rank of the prisoner. A king/sultan would never be executed (see: King Guy I of Jerusalem, King Louis IX of France, Emperor Baldwin I of the Latin Empire) but always ransomed, since it would net the captor an enormous profit. The same was also mostly true of princes, dukes, counts, etc., and even as far "down" as knights, assuming that their wealth and status were clear to see (in the confusion of battle high-ranking nobles could still be killed because they were not identifiable as being of their rank). There were exceptions, though, mostly if the captured nobleman had previously deceived, betrayed or otherwise done something to anger their captor (e.g. Reynaud de Chatillon was executed by Saladin because of his brutality against Muslim trading caravans). But this was the exception, not the rule. There are stories of Christian and Muslim nobleman captives living in fairly comfortable and indulgent captivity while they waited to be ransomed (and also, of course, the opposite in some cases).

As for non-noble prisoners, they were very rarely taken captive, unless to be made slaves (which was done by both Christians and Muslims, but mostly Muslims since the crusades took place in their part of the world and they had more immediate use for slaves). But since the average foot-soldier infantryman would likely be poor and have little to no wealth or possessions to his name, he was not seen as valuable. The standard practice was to kill these men unless they were to be enslaved, or if they were wounded to leave them there to die on the battlefield. This wasn't done simply out of spite or brutality, but also for the practical reasons of the captors often not having the resources for prisoners, be it men to guard them or food to feed them (often both). This was especially true of the crusaders, who generally had significantly less resources available to them than their Muslim opponents.

I've heard that both Saladin and Richard the Lionheart massacred prisoners. Was this a common occurrence or were these mass killings exceptional?

This was not something done regularly by either man, but happened in a very specific situation whereby Saladin was not complying with the terms of an agreement made between himself and Richard whereby Saladin promised to return the True Cross (which had been captured after Saladin's victory at Hattin) but he kept procrastinating doing so. Richard - and many of his soldiers - became angry and impatient, and so Richard had his captives - who were soldiers of Saladin's - all executed in view of Saladin's army in order to both pressure him to comply, and also show he was serious. Saladin retaliated by doing the same to his Christian captives. Both men still had high opinions of each other, though, and admired the iron will and ruthlessness of each other. While this appears shocking to us today, it wasn't seen as much at the time, with both Christian and Muslim writers at the time (or near enough) saying that while it was brutal and harsh, it wasn't unprecedented and both men were in their right to do it (a similar attitude existed in regards to the sacking/massacring of cities that refused to surrender during siege). I'm not aware of Richard massacring any prisoners after this incident, and neither with Saladin (although he did massacre all of the captured Knights Templar after his victory at Hattin a few years before).

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Sources:

God's War: A New History of the Crusades by Christopher Tyreman

The Templars by Dan Jones

Prisoners during the crusades could be killed, enslaved, or ransomed, depending on the circumstances. Enslaved prisoners often ended up being ransomed as well, eventually.

First of all, as Nostalgic_Summertime already explained, massacring prisoners was actually pretty rare - people made a big deal out of it because it was out of the ordinary. Massacres happened during the First Crusade, when the crusaders were apparently in an apocalyptic religious frenzy - or, in more practical terms, they just hadn’t developed a system to deal with prisoners yet. They could barely feed themselves, so they weren’t worrying about taking prisoners. At that point they weren’t even trying to get their own Christian prisoners back from the Muslims.

Nostalgic_Summertime dealt with Richard and Saladin’s mutual prisoner massacres during the Third Crusade so I’ll skip over that here. There was also a massacre of the inhabitants of Acre in 1291 when the Mamluks destroyed the city.

Prisoners were always part of the experience of crusading, but at first the crusaders either enslaved or killed their Muslim prisoners. They had no idea what happened to Christian prisoners, or how to get them back. There is a whole series of epic poems about Christian prisoners during the First Crusade (“les chetifs” - the captives), and there were legends about them - the sultan of Mosul was supposed to be the son of a Christian woman who was taken captive (this was the sultan Zengi, who conquered Edessa, which led to the Second Crusade). Throughout the 12th century both sides learned to expect that prisoners would be taken, and they developed a system to ransom prisoners and free slaves, which worked pretty well. Saladin, for example, negotiated the ransom of most of the inhabitants of Jerusalem in 1187. The notable exception, as mentioned, is when system broke down with Richard and Saladin during the Third Crusade.

If the prisoners were important enough, they could be kept in prison indefinitely or ransomed eventually - Reynald of Chatillon was held in prison for something like 15 years at one point, Raymond III of Tripoli was also imprisoned for about 8 years, and Guy of Lusignan was imprisoned briefly in 1187.

For less-significant prisoners, they would probably be enslaved. There are lots of examples of both Christians and Muslims being enslaved. In the crusader states, and in Spain, specific military orders (similar to the Hospitallers/Templars) were founded with a mandate to raise money and ransom prisoners/slaves. Muslims often felt that they should raise ransom money too. Ibn Jubayr and Usama ibn Munqidh frequently mention spending their own money to ransom as many slaves/prisoners as they could afford when they were visiting crusader territory.

Usama talks a lot about this aspect of crusading - sometimes he mentions raiding parties taking a few crusader knights back as prisoners, who were sometimes then killed. If they took larger groups they could be imprisoned/enslaved. Sometimes they would raid a crusader town and enslave the women and children. In one of his stories, a Muslim ruler takes a female Christian slave as his wife, but years later the woman managed to escape back to crusader territory. (Sexual slavery was a likely outcome for prisoners on both sides.)

The crusaders had the same fear: they were constantly worried about their Muslim slaves fleeing back to Muslim territory. Sometimes Muslims pretended to want to be baptized as Christians, so they could then be freed from slavery (as Christians were not allowed to have Christian slaves), but the crusaders didn’t want to baptize them. There were never very many crusaders, and their economy depended on slavery for agriculture and construction work. Christian pilgrims from Europe often mention seeing big groups of prisoners working in the fields or building a castle or some other construction project. So the crusaders clearly didn’t want to lose this enslaved workforce by letting them all be baptized, sincerely or insincerely.

Most likely, both Muslim and Christian slaves weren’t enslaved for life, since there was such an extensive ransoming network, and relatively easy opportunities to flee back to their nearby homes. Both sides could always get new slaves, with a raid into enemy territory, or after a battle, which happened frequently enough. So if you happened to be captured, and you weren’t killed right away, your life might suck for awhile, but your chances of being rescued/escaping were fairly high.

As for your question about vivisection...that seems extremely unlikely, to say the least. Let’s go with a hard “no” for that one!

Anyway, some further reading:

For prisoners, the best source is Yvonne Friedman, Encounter Between Enemies: Captivity and Ransom in the Latin Kingdom of Jerusalem (Leiden, 2002).

I don’t think there is anything specifically about the slave trade on the mainland, but for crusader Cyprus, there is Benjamin Arbel, “Slave trade and slave labor in Frankish and Venetian Cyprus", in Studies in Medieval and Renaissance History, n.s. 14 (1993), pp. 149-190.

For Usama’s anecdotes about prisoners and slaves, see Usama ibn Munqidh, The Book of Contemplation: Islam and the Crusades, trans. Paul M. Cobb (Penguin Classics, 2008).