If you want to maximize your damage as a warlock in a party, you should finish the mob using Shadowburn when there is too little time for another DoT or Shadow Bolt.
In duels, it is tempting to save the Shadowburn until you are sure that the opponent is about to die. A better strategy may be to use Shadowburn whenever possible, as this will result in a higher damage output.
Patches and hotfixes
Hotfix (2017-06-14):Shadowburn now causes Cremation damage, as intended.
Patch 7.2.5(2017-06-13): Shadowburn now generates 6 Soul Shard Fragments and an additional 6 if the target dies within 5 seconds.
Hotfix (2013-03-05):Shadowburn now properly generates 2 Burning Embers after killing a target that yields experience or honor.
Hotfix (2012-09-14):Shadowburn should always return a Burning Ember when it instantly kills the warlock's target.
Patch 5.0.4(2012-08-28): Now cost Burning Embers instead of mana. Deals Shadow instead of Shadowflame damage. Regains mana after 5 seconds, and gains Burning Ember on kill instead of Soul Shards.
Patch 4.3.0(2011-11-29): Now deals Shadowflame damage, instead of Shadow damage.
Patch 4.0.3a(2010-11-23): Damage has been reduced by approximately 12%.
Patch 4.0.1(2010-10-12): Changed. Only usable on targets with less than 20% Health. If the target dies during the duration, all three Soul Shards are refreshed. No longer requires a Soul Shard to use.
Patch 2.0.1(2006-12-05): Fixed an issue where the Warlock spell "Shadowburn" was improperly consuming two Soul Shards.
Patch 1.11.0(2006-06-19): If you cast Drain Soul while this aura is on the victim, you will no longer receive two soul shards upon the victim's death.
Patch 1.10.0(2006-03-28): The debuff which produces the soul shard upon death is now visble to the player and has a 5 sec duration. The Warlock will no longer sometimes receive two soul shards upon the victim's death. Targets which do not grant experience or honor will no longer produce shards. This spell will no longer apply its debuff to the creature when the spell is resisted.
Patch 1.5.0(2005-06-07): Honorable kills will now generate a Soul Shard when Shadowburn is used.