Limit Breaking - General rules of?

[LunaHoshino]

In general, Melee LB has the highest priority. You also don't want to save it until the boss is already at 1-2% (Because a lot of that damage will be wasted in overkill) - use it as soon as it's full, and safe to, on a given boss. If there are no melee, Caster LB should be used. If the only DPS are bards, what the heck, do whatever.

What Garlyle said. You really want to use it as soon as it's available (and safe to do so), because in some fights (especially endgame ones) it's possible to fill the LB gauge up more than once during the fight. The sooner you empty it, the sooner you can let it start building back up again and hopefully get another LB.

[Tint]

...and some boss fights will reset the LB bar to zero when the fight starts.

[Dualblade]

Melee LB: Used in most content, so be ready to use it a lot. Note that some people might take offense to you using it before the final boss (any of the LBs really, but Melee is most used.), but if you are able to get it back up to the full bar before then it doesn't actually matter that much.

Caster LB: Second most used, and any content that would have Melee LB used will have this used in its place if there is none. Some situations also see Caster LB being better than Melee (EX: During Copperbell second boss, Caster LB can pretty much immediatly wipe out the final little bits at the end, or in WoD, a LB3 caster can take out all three clouds that need to be killed if it starts before the barriers come up.)

Healer LB: Only used at LB3 for its Res ability. Take note that it rezzes people where they died, so it isn't as useful in certain situations like Titan. Bard also gets this one but its being changed for Heavensward.

Tank LB: Most underutilized, it sees the most work on new content...got to use LB3 version twice on the first day of WoD, and another time a week later...only group that survived that one, that was fun. Also apparently good for t13 at a certain point, but I haven't gotten into FCoB.

[Naria]

One thing to note that when you start doing any of the 24-man Crystal Tower raids (Labyrinth of the Ancients, Srycus Tower, World of Darkness) that the Limit Break resets every boss and basically every other fight in the tower is a boss. Because of this there is no point on sitting on the limit or building it to the third level in the tower outside of the final fight in World of Darkness. Once the boss is around 5% health use the melee/dps limit at whatever level it is built up at.

[KikoriL]

It's useful to learn when DPS limits can help push phases particularly efficiently, or when it's beneficial to group monsters...
Caster in Tam-Tara's final boss to drop the last wave of adds.
Caster in Haukke's final boss to drop the last wave of adds.
Melee in Qarn's Golem when the soulstone is shattered.
Caster in the last leg of Wanderer's Palace after the whole hall is pulled.
Melee in Halatali Hard's second boss to kill a Catobeplas' eye (if your team is undergeared and can't rush it).
Caster in Sastasha Hard's second boss to kill the enormous cluster of adds, or in the last leg to clear the whole hall.
Melee in Qarn Hard's second boss to kill the Sabotender Guardianguy.

These are just dungeon examples of when it's an excellent utility instead of a flashy killshot. Always circumstantial, since overgeared parties are common, but always possible and justified when the time's right.

[ChameleonMS]

Another reason to use the LB as soon as possible is that you reach 20% life threshold faster for all the special attacks (Misery's End, Assassinate, Mercy Stroke, etc...). This increases the DPS rate of all party members using these attacks.