The one distinguishing characteristic of a druid is the ability to shapeshift. This is their greatest strength and ironically one of their notable weaknesses. When the class was designed, the folks at Blizzard envisioned a protean opponent that constantly changed forms during an encounter. While the design didn't completely end up that way, with druids mostly keeping to one form suited for a particular task (e.g., bears when tanking), players get to see druids change shape more often during PvP. It's essential. Some of the best druids switch forms appropriately and often, although this can sometimes take a toll on their mana.
Druids are a hybrid class and thus enjoy the benefit of having three distinct roles and fighting styles which can confuse enemies at the beginning of a fight. Their shapeshifting, noted as their strength, is also their weakness here as it usually reveals their hand earlier than other hybrid classes because their forms are usually distinctive to their spec. A moonkin, for example, is obviously a ranged caster and likely to be an unsavory opponent in Eye of the Storm (stay away from the edge just to make sure).
By the same token, a druid is weakest in their normal (whatever passes for normal for a shapeshifting class, anyway), humanoid state. There is almost never a better time to beat down a druid as when they are in their Night Elf or Tauren -- and soon Worgen and Troll -- forms trying to cast a life-saving spell. Their various forms confer numerous protective benefits, and improvements to the moonkin and Tree of Life forms in the past have made for
irritatingly surprisingly resilient opponents. Fortunately for would-be druid killers, forms have some restrictions, too.
Moonkin, for example, are unable to cast any healing spells. This means that a Balance druid getting low on life should be expected to change form at some point in order to cast Rejuvenation or worse, Rejuvenation and Swiftmend. Other times, some druids will retreat into their Dire Bear Form while allowing a HoT to take effect -- an unusually mana-intensive, but sometimes necessary, recourse. Expecting these changes between forms is key to fighting druids: as a general rule, druids are strongest in their primary forms (e.g., Cat Form for DPS feral, Tree of Life for Restoration) and weakest when they are out of them. Catching them in humanoid form with a silence or stun is PvP gold.
The defining aspect of druid PvP is mobility. More than almost any other class, druids move around in combat not just because they must but because they can. One of the most powerful features of a druid's shapeshifting ability is the way it removes polymorph and movement-impairing effects, effectively making the druid the most elusive class in the game. With Travel Form, druids are able to free themselves from tight situations and easily create some distance between themselves and their opponents. In the rare instances where there's water involved, such as in world PvP scenarios (e.g., Wintergrasp), druids are unparalleled in their mobility with Aquatic Form and sometimes when glyphed for it, are -- pardon the term -- a class all their own. Needless to say, it is extremely imprudent to engage a druid in water.
In world PvP, in fact, druids even have the enviable option of instantaneous flight. Night Elf druids, in particular, can use the retooled Shadowmeld to drop out of combat and instantly shapeshift into flight form to escape the fray. Because Shadowmeld doesn't activate the global cooldown, it can be written into the same macro as a shapeshift. Obviously, because of their various transport forms, outdoor scenarios favor druids immensely and open areas are terrible places to engage a druid.
Although feral druids thrive in close quarters, having the option to flee is always best even for them... and no class is more capable of fleeing than a druid. It's virtually impossible to pin them down because of their ability to shake off movement-impairing effects, and then there's Dash, an ability that sees frequent use in Battlegrounds such as Warsong Gulch as druids make their way out of the enemy base.
All druids regardless of spec are capable of disappearing with the Prowl ability. Sometimes throughout a fight, druids will create some distance and exit combat, enter stealth, and reappear when it's most beneficial to strike. This isn't limited to the rogue-like feral druids, either. It takes tremendous effort to pin down and catch a druid off-guard, and is often only pulled off with coordination and precision as demonstrated in Arenas. The ability to flee, disappear, and reposition is essential to druid PvP which makes them terrible candidates for a first target in a group.
It's always important to remember their natural ability to shrug off polymorph and movement-impairing effects, so it's just a waste of resources to target them with these things. It won't even slow them down. We've only barely touched the surface as we now have an idea of what druids are like. We haven't even gotten to the part of all the hurt they can bring to a fight.