Strengths & Weaknesses
The druid’s biggest PvP strength is versatility. This comes through the various forms available to the druid, and allows a druid to adapt to any situation in a pinch. While some druids are not particularly proficient at dealing damage, most can outlast virtually any other character. Often players will get bored of fighting before they kill you.
Travel Form is without a doubt one of the best PvP abilities in the game. After lvl 30, you really shouldn’t have much fear of a ganking, because it is so easy to escape. Pop Rejuvination/Regrowth, switch to travel form, and don’t look back. Most players won’t be able to catch you. Travel Form is also excellent for Warsong Gulch, where druids are essential, being the main flag bearers.
Switching forms costs a fair amount of mana, but it is the key to winning battles. Dire Bear is excellent against melee classes, and gives you a free heal. It also has a stun, which gives you an opportunity to cast another heal.
Stealth (in cat form) gives you an immediate advantage. Use it to get some damage before they can react, or to time your entry into a group battle. Feline Swiftness is faster than Travel Form, if you really need an immediate speed boost.
While druids may lack in outright DpS, they are excellent support and can fill almost any required role in PvP. They are quite dependant on mana, so spells like Viper Sting are quite good to apply. Don’t bother with Polymorph or any slowing spells (aside from pulsing spells, like Earthbind Totem and Frost Trap), because shapeshifting removes those.
General Strategies

Entangling Roots is a great ability in solo play against most classes. You can use it to gain some distance, or to cast a spell without being interrupted. Use it to kite your opponents. After casting it, switch to Travel Form or Cat form and get some distance.

Moonfire is the only instant-cast damage spell without a cooldown, and can be spammed. This is inefficient mana-wise, and is not advised. While it may seem like you can kill someone with it, you are often better off healing yourself or rooting them, and using a more proficient source of damage. If you try and kill someone from full with Moonfire, you will run out of mana before they run out of health.
Hibernate works on PC’s as well as wild beasts. This means it is very useful against hunters. However, it is often overlooked against other druids (in all but Moonkin form), and shaman in Ghost Wolf form (this is most often overlooked, and can really confuse people when you cast it on them). If your opponent has no DoT’s on them, you can use this to heal yourself while they are crowd controlled, or to take out an opponent in a group battle.
Innervate, now that it is available to all classes, is an important part of PvP. Mana equals health, because of the druid’s ability to heal. You will often find that your mana drains before you can kill your opponent, especially against another healing class. This is where Innervate shines. It is less useful against priests, shaman, and warlocks with a Felhunter out, as they can dispel the buff, but nonetheless, it is still a very important part of your bag of tricks.
Removal of poisons and curses is an often overlooked but essential part of playing a druid. This applies to yourself, as well as your teammates. These spells cost only a small amount of mana, but can prevent a large amount of damage (or remove an annoying poison effect). Don’t forget to use them.
Macros
Nature’s Swiftness + Healing Touch
This will cast both without triggering the global cooldown. You can change the rank of the spell depending on your level. It should also keep your target.
/cast Nature's Swiftness
/script SpellStopCasting();
/cast Healing Touch(Rank 10)

/script if ( SpellIsTargeting() ) then SpellTargetUnit ("player"); end
Innervate + Retarget
This will cast innervate on yourself and retain your target.
/script TargetUnit("player")
/cast Innervate
/script TargetLastTarget()
Arena
Druids in Arenas are generally best used as healers. With some resilience and backup healing, druids can be very powerful. If you are getting beat on, you can switch to Bear and bash/heal, or Travel Form and run to a safer location (this is particularly effective in Nagrand, which is larger and more open than Blade’s Edge).
Druids are powerfully for one simply ability: Cyclone. This is undispellable, uncounterable CC that lasts 8 seconds with diminishing returns. Not even paladins can use their immunity to remove it. It can’t be used on Divine Shielded paladins, but their shield will not remove it if you get there first. This can completely destroy a team, by removing at least one healer you are going to have a huge advantage.
Feral druids suffer in arenas because they have small mana pools, and need to be on top of a player to do damage. Although shifting removes snares and slowing effects, doing this repeatedly costs lots of mana.
Moonkin druids are actually quite powerful here, because they can use cyclone, and switch out to heal if things get hairy. They can provide pretty good damage, crowd control, and have pretty good survivability too. Paired with a healer in 2v2, for example, they are an excellent choice.