In Game

Kain is a useful character, though he rather tapers off late-game, he'll save your bum pletny of times when you get him for the second times. His special skill is Jump, which allows him to do double damage over two turns, remaining invincible while in the air. Basically, while Cecil does heavy damage and absorbs heavy damage, Kain does heavy damage and takes as little as possible. He can equip heavy armor and he tends to have a few levels above the party average. He can also equip swords and axes, but spears are your best bet for Kain by far. His spears are:

Spear
Atk: 9 - Hit %: 50
Obtain: This weapon is initially equipped.

Wind Spr
Atk: 55 - Hit %: 33
Obtain: When Kain rejoins your party at the Tower of Zot, he already has it equipped.

Fire Spr
Atk: 66 - Hit %: 30 - Special: Fire elemental
Obtain: You can buy it in Agart for 11000 GP. It can also be stolen from Flame Men in the Tower of Babil, and sometimes it is dropped by them.

IceSpear
Atk: 77 - Hit %: 30 - Special: Ice elemental
Obtain: You can find it in the Tower of Babil, or you can buy it for 21000 GP in the Cave of Eblan.

BloodSpr
Atk: 88 - Hit %: -28 - Special: Drain
Obtain: You can find it in the Castle of Eblan.

Gungnir
Atk: 92 - Hit %: 30 - Special: Vitality +15
Obtain: When Kain rejoins your party for the final trip to the Moon, he already has it equipped.

Dragon
Atk: 99 - Hit %: 30
Obtain: Dropped by Red and Blue Dragons.

HolyLnce
Atk: 109 - Hit %: 40 - Special: Holy elemental
Obtain: Defeat Plague in the Final Dungeon.

Abel's Lance
Atk: 228 - Hit %: 35 - Special: +15 Str, +15 Agi, +15 Spr, randomly casts Tornado
Obtain: Lunar Ruins, Final Fantasy IV Advance only. Also makes him totally viable again.

One strategy I use with Kain is sticking him in the back row and having him "Jump". This cuts down on damage he takes, and he still does his normal amount jumping. Also, in Final Fantasy IV Advance, Kain has access to the Dragoon Gloves, which change "Jump" to "Double Jump", essentially quadrupling his attack power. Shame about the damage cap, eh?

In order to get Holy Lance, you have to fight Plague. You might have to fight this battle quite a few times before you can kill this guy off. Why? He immediately begins a countdown timer on your entire party, giving you a very limited amount of time to kill him. So in order to beat him, you have to use quick attacks which are quite powerful. The only way I could do this was by casting haste on Kain and attacking with jump (jump does a lot of damage to aerial monsters, and Plague is an aerial monster) and by having Cecil and Edge attack normally. As for Rosa, she should be casting haste as much as possible, and Rydia should use whatever spell/summon you think is most powerful. If you have it, Rosa can also cast Holy to get the extra damage in. The reset button is your friend.

In order to get the Abel Lance, you have to complete Kain's trial, which I am told is awesome and plot-based, however, I don't have FFIVa, so I can't really talk about it. I don't think it's harder than Plague though.

Kain also makes a boss appearance in game. However, he's garunteed to win (damn straight!) and so, there isn't much strategy I can give you.

Kain is fairly unique among FF characters in that there is a recurring item named for him. Kain's Lance is available in Final Fantasy IX and in Final Fantasy X. In FFIX, it's one of the best weapons available for Freya, the party's resident dragoon, and it teaches "White Draw", "Dragon Crest" and "Cherry Blossom".