This is a guide about all of the special attacks you can do with unique weapons in the game. Effect description data taken from Runescape.com.

Item	Effect	Power Cost	Picture
Abyssal whip	Energy Drain: This attack is more accurate and, if successful, will transfer 10% of your opponent's run energy to you.	50%
Darklight	Weaken: This is an ordinary attack which, if successful, reduces your opponent's attack, defence and strength. It is twice as effective against demons.	50%
Dragon 2h sword	Powerstab: This weapon produces an area attack which does damage to nearby enemies.	60%
Dragon axe (hatchet)	Clobber: This attack dazes your opponent, lowering their defence and magic stats.	100%
Dragon battleaxe	Rampage: +20.5% Strength, -8.8% Attack, -8.8% Defense, -8.8% Magic, and -8.8% Ranged	100%
Dragon dagger	Puncture: This attack consists of two quick strikes at your opponent, with slightly increased accuracy and damage.	25%
Dragon halberd	Sweep: Sweep: A devastating slash through your opponent. For large monsters the halberd will automatically sweep back and forth to do extra damage or will hit two opponents in a multicombat area once.	30%
Dragon longsword	Cleave: This attack is more powerful and so inflicts increased damage to your opponent.	25%
Dragon mace	Shatter: This attack is much more powerful, but it also has a reduced chance to hit.	25%
Dragon scimitar	Severe: This attack is more accurate and, if successful, will prevent your opponent from using protection prayers for 5 seconds.	55%
Dragon spear	Shove: This attack deals no damage to your opponent, it simply forces them back away from you and stuns them for a short time.	25%
Excalibur	Sanctuary: +11.8% Defense	100%
Granite maul	Quick Smash: This is simply an extra attack taken instantly with no other effects.	50%
Magic longbow	Powershot: This attack uses the full power of the longbow so that the chances of hitting your opponent are greatly increased.	35%
Magic shortbow	Snap-Shot: This attack allows you to fire two rapid shots at your opponent, however the speed reduces your accuracy.	55%
Rune claws	Impale: This attack is more powerful and more accurate, though it is slower than normal.	25%
Rune thrownaxe	Chain-Hit: In a multiway combat area this attack bounces the projectile between several targets, dealing damage to each of them.	10%
Seercull	Soulshot: This attack reduces your opponent's Magic level by the amount of damage you inflict.	100%
Barrelchest anchor	Sunder: This attack doubles your chance to hit. A successful hit will lower either your enemy's Defence, Attack, Ranged or Magic level by 10% of the damage caused	50%
Dorgeshuun crossbow	Snipe: This Ranged attack will lower your opponent's Defence level by the amount of damage you inflict. You will have a very high chance of hitting an unsuspecting opponent	90%
Bone dagger	Backstab: This attack will lower your opponent's Defence level by the amount of damage you inflict. You will have a very high chance of hitting an unsuspecting opponent	90%
Brine sabre	Liquefy: Only useable under water. Doubles the chance of hitting, and adds a quarter of the damage dealt to your Strength, Attack and Defence	75%
Magic composite bow	Powershot: This attack uses the full power of the longbow and will have an increased chance of hitting your opponent	30%
Ancient mace	Favour of the War God: If this attack hits it will inflict normal damage even through the 'Protect from melee' Prayer. It will recharge your Prayer energy by the amount of damage done while draining your opponent's the same amount	100%

How to use them effectively:

I recommend to use these when you are either pking, dueling, or fighting a strong monster.

There is one really neat way to use the dragon battleaxe without losing other stats. What you do is first use the special attack then drink 1 dose of stat restore potion. This will still give you +20.5%strength but with no other lost stats.

The dragon dagger (p) is great in duels and pking since it poisons your opponent, while the normal dragon dagger is almost as good with quick hits.

The Dragon Spear is very effective at stunning your opponent and therefore good at pking and duels.

The Magic bows (especially longbow) can also be used well as a first attack against monsters such as dragons. After the first attack you can switch to whatever bow you prefer.

One Rune weapon that has a special attack is the Rune Thrownaxe, a seldom used weapon. It is effective in a crowded area as it exerts a chain reaction of damage, almost like a cannon going off.