A lot of folk like the television version of Highlander, I'd guess more than the movies. And some people have RPG campaigns featuring Immortals. Rather than try to give stats for Immortals in every RPG system I'm familiar with, I'm going to try to examine the "why" of the Immortals and how that can fit into a campaign. What is really going on with these strange people?
This seems to be the "official" story. God or the Universe is selecting a future ruler of the Earth by having Immortals live, learn, gain something from killing other Immortals, and ultimately leaving one who will have all their power and knowledge. The divine origin would seem to be supported by the fact that even the most evil of Immortals will not violate Holy Ground. The problem with this is the illogic of the Ultimate Ruler being determined by sword skill. Even if this is not the "truth", it does seem to be what the Immortals themselves believe.
I've seen little evidence that an Immortal gains much of anything other than a real rush from killing another Immortal. The only example of a real change in an Immortal after a Quickening was Darius who went from being a warrior to being a pacifist priest. Perhaps there isn't much of a change unless the first Immortal is incredibly powerful, and the use of the knowledge isn't gained until one gets the Prize. However, the episode "Dark Quickening" established that Quickenings from enough evil Immortals could potentially make a good person evil; perhaps it depends on the strength of the Immortal's own conscious and unconscious personality.
Following this idea Immortals don't get a lot out of killing other Immortals so PC Immortals would acquire little more than a reputation and perhaps enemies. Of course other party members would notice the fireworks when he or she killed another Immortal and would probably have a lot of questions.
Think about it. How does an Immortal know about the Gathering or the Prize? Somebody tells them. It is not inner knowledge. There's no way to prove otherwise until there is only one Immortal left. But who knew about it first, and how did they know? Sure, one could argue that the Quickening is evidence but it could just be a side effect of killing an Immortal with no real lasting effects, usually.
What if it is a story the Watchers or some unknown group made up to keep down the number of Immortals, and to prevent them from establishing an Eternal Empire ruling the mortals? Some Immortal was told of the Prize by a supposed sage or wise man or priest and told others. Immortals seeking a meaning to their extended, childless lives believed, and newer Immortals assumed that the elders knew what they were talking about.
Of course this begs the question; what are the Immortals then? They're just a random mutation. Humanity is evolving towards immortality, but so far all immortals have been infertile and the genes haven't joined the general pool.
Also possible is that the Watchers or another group produced the Immortals through breeding or some incredible form of genetic engineering. Could be aliens or the Illuminati or whatever your favorite secret group is. Obviously the PCs shouldn't know this, at first.
This is the premise of Highlander II: The Sickening, um, Quickening; they are from the planet Ziest and are on Earth for no good reason and, darn that is a bad film begging for the MST3K treatment and is not "canon" for the rest of the series. But under this assumption the Immortals are aliens dropped off on Earth for some reason or another. There probably isn't a Prize, but there could be. They could be like The Midwich Cuckoos (movie version, Village of the Damned) in which children born to Earth women are actually aliens whose genetics are sent from a distant world. The aliens may want to help humanity develop, or they may just want their seed on many worlds. Possibly the real purpose is lost.
Arthur C. Clarke wrote a story in which an alien spaceship crashed on the Earth and the aliens placed their consciousness in an earth creature. Unfortunately, the consciousness got diffused into several individuals and the only thing remaining is a desire to go to the site of the crash which is under the North Sea. The descendants of that original creature are of course lemmings.
This provides an explanation for just why there is a need to kill Immortals and why this energy flows into the victor. They are trying to become "whole", although they may not know this. While this premise could work in an SF campaign, I think it works best in a fantasy setting. It lends itself pretty well to the RuneQuest "Glorantha" setting, as chopped up gods are already part of the mythos. In Glorantha, the victor would have the vanquished's POW added to his or her own. Gradually, they would regain their god powers and when they were Complete, they'd be restored to their place in the universe. I would say that the Immortal should be an NPC as the Immortal is going to become very powerful. Unless the other players don't mind their PCs becoming the servants of another very powerful PC and know about this when the campaign starts I'd not have a PC Immortal.
This could be rather interesting as the PCs help rebuild the god. What if their patron who claims to be a part of Genert, the benevolent earth god is actually a part of Gbaji/Nysalor the dreaded Illuminator or worse, a part of Wakboth the devil?
I will note that I've not tried any of the above campaign ideas but if anybody does send me a note or something. :)
Since I wrote the original version of this essay, Highlander the series has ended with a lame "It's a Wonderful Life" take off, and the ultimate question of what the Immortals really are and what the Prize really is remains a mystery. Of course there's going to be the spin-off series, Highlander: Raven featuring Elizabeth Gracen (Amanda); maybe it or the future movie will deal with it.
I would personally like a resolution that establishes that, yes, the Gathering really is a scam perpetuated by the Watchers millenia ago to keep the Immortals from taking over the world. The Hunters who actively killed Immortals knew this, as do most high position Watchers, but didn't trust the Game to keep down their numbers and to prevent cooperation between Immortals. That's the answer that makes the most sense. We shall see.