Cain & Abel
Cain and Abel were the two sons of Adam and Eve - Cain being the elder. Their story appears in Genesis.
Cain was a tiller of the ground, and Abel a keeper of sheep. Both brothers brought offerings to God. Cain's offering was fruit and Abel brought lambs. God appeared to favour Abel's offering over his brother's, something that angered Cain greatly. In a jealous rage, Cain killed his brother. (Depending on which religious text you are reading, Cain may also have killed his brother over a woman.)
God - being God - was less than impressed with this, and Cain was cursed and marked as such. He would never again be able to till the earth, and would be "a fugitive and a vagabond."
"The voice of thy brother's blood crieth unto me from the ground"
...is what God says to Cain. There was a point when Kain would have killed his almost brother, all because of jealously. And Kain's "curse" is to commit himself to Mt Ordeals and train far away from everyone, in self imposed exile.
Cain's name can also mean spear, so I'd like to think it isn't a coincidence that Cain Highwind was named as such. The change to Kain in the English version was probably due to Nintendo wanting to be as inoffensive as possible (after all, the Holy spell in FFVI was renamed to Pearl in the original North American SNES release, just for another example of Nintendo's early policies on such things).
The GBA remake of the game has a new weapon for Kain - Abel's Lance. This lance is originally known only as "The Blood Soaked Lance" due to it being a mysterious murder weapon that appears to haunt Kain. It transpires that it is the dark part of Kain performing the killings, and it's only when he overcomes this darkness that the lance becomes something shiny and wonderful. See also: The After Years.
Cain was the original name for our much beloved dragoon in the Japanese release. He was renamed to Kain in the English games.
Cain has a lot more meanings associated with it than Kain. Aside from the biblical connections to Cain and Abel and the parallels that can be drawn from that, Cain can also mean a fixed spear or a lance ready to strike through. Now, how interesting is that? This makes it obvious - to me, at least - that Cain is his original and strictly correct name, and it's also so incredibly suitable it makes me gleeful. Yet another meaning for Cain is artisan or craftsman, and these are both Hebrew in origin.
The first name Kain has no particular meaning, although it is an Irish surname. It can be spelt in various ways, the most common I've seen personally is Kane and it's variation Keane, although Cain, Cahan, O'Kaine and various others are all used. This name can mean clear or fair, and probably has nothing to do with Kain himself at all. The word cain in the Irish language means penalty or condemn.
Gungnir, aside from being one of Kain's weapons, is the name of Odin's spear in Norse mythology. It was created by a dwarf named Dvalin. This weapon is unrelenting, and never misses it's target. It ceaselessly slew the enemy and always returns to Odin's hand after it has been thrown. Gungnir is represented by the runic symbol Gar, which you can see to the left.