Pretty much every healer have the potential to put out some burst damage on demand. There will be moments in both PVP and PVE where this is handy. Mostly in PVP, of course, where the ability to burst down an enemy can be viewed as healing saved. But not exclusively, there will be times in PVE when bursting is handy. For example if you pull aggro on some add and it is mostly dead already or have low health, or on bosses which have vulnerability periods in which every point of damage counts. Take the Headless Horseman, to take an example a lot have experienced.
The main difference between bursting in PVP and PVE is the risk of getting counterspelled/kicked and thus getting that school of magic locked out. This is only a serious problem on your healing school (holy or nature) and only on spells with a cast-time. Actually, it's often an advantage to get your non-healing spell school locked, because whoever blew that cooldown can't immidiately counterspell you again. In both PVP and PVE you risk getting your casttime extended by damage taken for non-instants.
For all of the bursty combinations, you want to maximize the damage output for the given amount of time. The question is, how much time do you have? You can make several combos depending on how much time you have at your disposal. There's also an advantage to put an instant at the end of a chain, because it hits the same moment as the cast-time right before it, and the global cooldown triggered doesn't "count" towards the time the combo takes. In PVP, many enemies will hit defensive cooldowns if they take incoming serious damage. By making the damage hit at the exact same time, they won't have time to react between the nukes.
I ignore spells with long cooldowns. Though you can get a nice burst as a shaman by for example using Nature's Swiftness and Chain Lightning, you usually want to save those for other purposes.
A quick and safe 1.5 sec combo is Mind Blast -> Shadow Word: Death. If you don't risk getting counterspelled, Holy Fire -> Shadow Word: Death will probably yield better damage for a holy or disc-specced priest, at a lower mana cost.
You can of course drop both for a twice as long combo, Holy Fire -> Mind Blast -> Shadow Word: Death. I like using Holy Fire first because it packs a dot, slightly longer cooldown and better damage if you can't finish the combo.
If you're discipline, you also have the option of dropping Penance into the fray, of course based on the assumption that you don't immidiately need it for healing. If you're holy, pray for a crit and drop an instant Smite in there.
All in all, priests got pretty good burst potential, and at a neat 30 yard range. Use it well.
Druids are lacking in the bursting department. First and foremost, the problem is that to deal any kind of damage (except Thorns) you need to shift out of tree form, which means that the mana cost of the combo is sort of increased by the mana cost of shifting back to tree form.
The next problem is their spell selection. I don't assume any healer specs Starlight Wrath. Starfire deals decent damage and doesn't include any risk of counterspelling, but at a 3.5 sec casttime. Wrath deals pretty low dps without serious talent investment into the balance tree, risks counterspelling, and still has a 2 sec cast time. Moonfire deals very abysmal damage compared to it's mana cost when only looking at the instant part.
There's always the option of Moonfire spam, which has the advantage of being only instants. However, mana cost and low dps doesn't make it a too powerful burst.
The only option they have is to chain Starfire -> Moonfire or Wrath -> Moonfire depending on how long time they have.
All in all, druids are seriously lacking burst potential, in my opinion.
Shammies have some interesting options. First and foremost, Lava Burst is a garantueed crit as long as the enemy has Flame Shock on them. Lava burst deals better damage at a significantly lower mana cost than Chain Lightning, even without Flame Shock present. In addition it's handy that it's not from the nature (healing) school, in case of counterspells. Like Lightning Bolt it has a travel time, which can be both a blessing and a curse.
The special thing about shocks is that they share the same cooldown. In PVP, if you *need* your enemy snared (Frost Shock) or the shock cooldown ready to interrupt a spell (Earth Shock or Wind Shock), you won't have the option of chaining Flame Shock into Lave Burst. In PVE, you might often be better of using Wind Shock to reduce aggro rather than use it for a nuke. There's also the problem with range, 20 yards (barring gear bonuses) rather than 30 yards on cast-time nukes.
All in all, there's a lot of different combos for different needs.
First, let's look at Flame Shock -> Lava Burst. Since you have to wait for global cooldown after the first, the combo takes 3.5 sec, barring haste and interruptions. While Lava Burst is a garantueed crit, without Elemental Fury it's only a 150% crit, and the initial hit from flame shock is nothing great. In effect, while handy, this isn't a superior combo. The redeeming trait is that you only need to stand still to cast in 2 of those 3.5 seconds. Glyph of Shocking reduces the time of this combo by 0.5 sec.
If you spend 4 seconds, you can chain Lava Burst -> Chain Lightning -> Earth Shock. Frost Shock at the end deals a bit less damage, but snares if you need that should the combo fail to kill. The advantage of this combo is that Lava Burst have travelling time while Chain Lightning and Earth Shock hit instantly, meaning they can hit in very short amount of time (<0.5 sec), giving an enemy player very little time to react, provided you're at max shock range. If you're in melee, this isn't such a good idea. Of course, there's the risk of getting Chain Lightning counterspelled. Just Lava Burst -> Earth Shock is a quick and safe combo, in the sense that you can't get nature counterspelled.
Given the nature of Lava Burst, the best option for bursting is setting up a killer combo by casting Flame Shock earlier, then load up a double or triple nuke so that you get a second shock in. This is easier said than done in PVP, slightly less so in PVE.
Since pallies lack any casttimespells, their nukes are limited only to the instants they have. The interesting part is that Judgement of Justice (or any of the other judgements) is off the global cooldown, meaning you can that and another instant in at the same moment. Seal of Righteousness is probably the seal that causes the best damage on jugdement for a holy pally. Enlightened Judgements give judgement a lot of range, in fact more so than most other offensive spells in the game.
The primary nuke is Holy Shock, which has a few disadvantages. Only 20 yard range, for a start, and the fact that you might need it for healing rather than damaging. The bright side is that you probably have a fairly good crit rate on this, and using it with Divine Favor still grants the instant Flash of Light when used offensively, thanks to Infusion of Light.
Chaining Holy Shock and a judgement gives a fairly good nuke, and is completely instant. From 3.1 you can also throw in Exorcism, which will then be usable on all targets rather than just demons and undeads. See here for more details if you missed the change.
I believe Blizz doesn't dare to give druids a baseline high-damage, low cooldown ability like Holy Fire, Mind Blast and Lava Burst because they're afraid that it might make druids overpowered in PVP (again).