Addhp
Addhp is a not so much a damage type, but it can hurt. And was originally intended to be an interesting challenge added to creatures that for one reason or another were not hard enough all ready. In this modern era of 3k, Addhp is common to the point of hundreds of mobs being capable of attacking with it, and half the guilds having powers that can do it. Several weapons also deal addhp damage.
Addhp comes in two flavours, vanilla, that is Addhp1, and something a little more exotic, Addhp2. There is some dispute on what Addhp2 is actually defined as. It depends which player you talk to.
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Addhp
Damage that bypasses all armour, yet by itself cannot kill. If the damage drops you below 1hp, it will actually heal you a small amount in some cases. (Only to take it away again.)
Addhp2
Similar to Addhp. If you have overmax hp or sp when hit by addhp2 it sets you to your maxhp or sp and then normal addhp commences. Every example of this I've seen is on Tensor's mobs only, also most poisons do this type of damage. Generally has the ability to kill you unlike addhp.
Reflect Damage
By nature, almost all reflecting damage is dealt back to you as addhp. There is some exceptions to the rule. And it follows my definition of 'addhp1', as opposed to addhp2. Many examples of reflect mobs can be found in areas coded by Tensor and Rastafan.
Addsp
Same dealy, but Sp. I don't personally know if what I would call 'old addsp' exists, and of course it would make no sense that something I would call 'addsp2' exists at all.
Guilds that can currently deal addhp damage: Necromancers, Monks. Bard noxious cloud isn't addhp by definition, but rather lowers an opponents Dexterity, Constitution and Strength by 3 points each while in effect. For some enemies, it can also do a few hit points of damage each round while active.
Some weapons that can deal addhp damage: Vorpal Blade, Blade of the Damned, Staff of the Magi, Wraithvein, BloodThorn, Weapons of Wounding