Okay, let's get some things straight here:
Mercenaries, for the sake of this discussion I will separate into three categories: antiquity, medieval, and modern.
1. Antiquity mercenaries, as 75% points out, are most used, or at least the most noticeable, around the time of the Punic Wars. Carthage, being a very mercantile nation, hired mercenaries to fight their wars, because that's how they fought their wars. Hamilcar Barca, was noted to be one of the very best mercenary leaders out there, to the point he turned his group of mercenaries into loyal soldiers of the Barca family. His son, Hannibal, would later be known as the guy who gave Rome a run for their money later down the line.
So while indeed, some antiquity mercenaries are dickbags like the Mamertines, as what we can see during the Punic Wars and after, until the fall of Rome, mercenaries came in a variety of traits. You got your professionals, your mediocre ones, your backstabbers, and your bandit armies. Seeing this is antiquity, a time where professional soldiers are rather common, then mercenaries were not used as much during the Free Company reign of the 14th century in Italy.
The Condeotierri would simply refuse to fight the enemy, which is close.
Condottieri were simply the captain, general, or leader of a free company. It's more or less a blanket term for 'leaders of Free Companies'.
2. Medieval mercenaries, too are like the ones in antiquity. But what most people remember them for are their involvements in 14th century Italy, around the Late Middle Ages/Early Renaissance period. The Hundred Years Wars has ended, England and France have for the most part disbanded their armies, and now you've got violent men who are really good at killing without a job. Thus they became, for the most part, bandit armies. The more professional ones are the ones people remember, the famous or infamous Free Companies.
Among these famous mercenary companies were Great Company from Germany, White Company from England, and Catalan Company from Spain.
Then, were there notable mercenaries band which would, while under contract, and with their employer still able to pay them, would defect if an enemy offered them a better pay?
Well yes, and no. Out of the Free Companies, White Company was known as the most trustworthy. But that said, John Hawkwood, still switched sides like six times during his years in Italy, from Pisa, to Perugia, for the Papacy, all the way until his last round with the Florences until his death, White Company more or less was disbanded after that.
Now, the thing about the Free Companies is that they WERE total assholes douchebags. As, this quote verifies:
"A multitude of villains of various nations associated in arms by the greed to appropriate the fruits of labor of innocent and unarmed people, let loose to every cruelty, to extort money, methodically devastating the countryside ..." - Pope Urban V.
White Company, THE most trustworthy (really shows to you the quality of these mercs) of mercenaries, were hated by many, and at one point, each member of the Company was offered a bounty of 30 florins for each member killed.
These Free Companies would travel around Italy, threatening to sack a city if they don't pay them with loot or food. Thousands of men not working on the fields and taking food from honest farmers? You can see why Pope Urban called them total d-bags.
And this is why Machiavelli's the Prince was thought of as a satire, because people at this point had no proper standing army, unless you were Spanish or the Ottomans. While it was possible for these Companies to be beaten by townsfolks, as shown when the Perugia and Sienna beat back White Company, they always came back Alfoso Profeessione once wrote describing the Free Companies, "a hydra with a hundred heads, once one was defeated, there was always another." Truly, these communes who won these battles won Pyrrhic Victories.
3. Modern mercenaries of today are more or less security guards with military grade equipment.
Sure, you got the terrible Executive Outcomes and their heinous crimes, but as bad as they are, I think most of you would rather deal with them or Blackwater/Xi rather than the Free Companies.
Any respectable Private Military Company would hire men of military background, of good physical and mental health, and you know, NOT psychopaths. Because psychopaths are bad business. Modern mercenaries of today are decent people who spend their time in exotic countries guarding stuff, people, and performing combat roles for the government/faction they're working for. See Blackwater and their involvement in the Iraq War.
So no, modern mercenaries are NOT Far Cry's mercenaries.
Here's a handy PDF if you want to read more about the Free Companies, and here's an excellent documentary called
Mercenaries In The Modern World if you have an hour and a half of free time to learn about the soldiers of fortune of today.
EDIT: I should note that I left out Swiss Pikemen for a reason, and that's because these dudes deserve a post of their own.