Some spells are especially useful for killing Heroes.

Humans

Paladin - Holy Light - Great on Undead Heroes, Dark Ranger, and Pit Lord
Mountain King - Storm Bolt - Storm Bolt throws a hammer across long distances allowing you to severely damage the enemy Hero without actually being next to him. The Mountain King also has a Stun ability which will allow other units to surround and beat on the Hero while the Hero is stunned.
Blood Mage - Banish - It not only slows them so you can catch up, but it will also make your other hero killer spells do more damage.
Sorceress - Slow - Slowed Heroes are much easier to catch. Make sure you deactivate autocasting of slow so that you may save mana to cast slow on heroes.
Orcs
Raider - Ensnare - With several Raiders you can keep the ability going for quite a while by recasting it.
Far Seer - Chain Lightning - Rips Heroes up!
Tauren Chieftain - Shockwave - This is also helpful when other units are lined up in the path of the Shockwave.
Shaman - Purge - Purge slows the target and strips beneficial buffs. Since Heroes are very fast, slowing them can allow you to catch up and kill them before they can get away. Be sure to deactivate Autocast spells so a Shaman has enough Mana to continually Purge the Hero until they are dead.
Shadow Hunter - Hex - prevents them from casting spells

Night Elves
Dryad - Slow Poison - Since it only lasts 1 second on Heroes you will need multiple Dryads firing at the enemy Hero to keep them continually slowed.
Keeper of the Grove - Entangling Roots - Stops a Hero from attacking, moving, and does damage to them while they are stuck.
Demon Hunter - Mana Burn - Mana Burn drains Mana and Health from the enemy Hero.
Demon Hunter - Immolation - If you can trap an enemy Hero next to the Demon Hunter using Immolation, you can make quick work of them.
Priestess of the Moon - Searing Arrows - Higher levels of Searing Arrows combined with Items and her Aura can make quick work of Heroes.
Warden - Blink - Blink ahead of the Hero that is running away and kill it
Warden - Shadow Strike - Slows the enemy Hero and damages it
Warden - Fan of Knives - Good finishing spell to use on enemy Heroes as they are running away
Mountain Giant - Taunt - Causes the enemy Hero to return from running away and fight. Sometimes the enemy doesn't notice and you can use this to kill their Hero while they are not paying attention.
Druid of the Talon - Cyclone - It will let your army surround where the enemy Hero will drop.
Undead
Dread Lord - Sleep - Sleep is a very annoying spell for enemy players. Simply put their Hero to sleep. The enemy can wake their Hero up by attacking it but many people don't think about doing that, or it takes them a while. While the Hero is asleep, surround it with units so it can't get away then focus fire on the Hero. If you surrounded them properly there will be no escape.
Dread Lord - Carrion Swarm - This can be very effective against enemy Heroes if surrounding support units don't soak up the damage. Try to get the Hero off on its own, and then use this spell.
Death Knight - Death Coil - This can be used to suck life away from enemy Heroes. This can be cast on Heroes from some distance away.
Lich - Frost Nova - Cast this on an enemy Hero to damage and slow it.
Necromancer - Cripple - This spell severely disables Heroes. Use it!
Crypt Lord - Impale - Stops the Hero and throws it up into the air!

Neutral Heroes
Naga Sea Witch - Frost Arrow - Slows the enemy so they can't get away as easily.
Dark Ranger - Life Drain