This one seems to come up pretty regularly, mostly because Druids look very good on paper, however in actual play they have a few weaknesses when compare to other classes (namely Shaman).

PVE:
Pros:
- Can cover all 3 roles (Tank / DPS / Heals)
- Some complimentary buffs
Cons:
- Eclipse procs difficult to manage on multiple toons
- Buff stacking not a good as some other classes (Shaman, Pallies)

Managing Eclipse procs are the biggest problem for a PVE team, since they equate to a ton of damage in PvE. You can get by in Heroics ok, but you won't be competitive in raids if you can't take advantage of them.

PVP:
Pros:
- 5 x Starfall is OP
- 5 x Treants is great against melee targets
- Hurricane best targeted AoE in game (esp deadly when combined with Starfall)
Cons:
- Outside of Starfall, lack of burst in PvP
- have to drop form to heal
- vulnerable to fear
- no way to mitigate incoming spell damage / lack of interrupts

There are several drawbacks for druids in PvP - while Starfall and Treants are great, outside of this Druids really suffer from a lack of burst. This is especially noticeable against high resil targets, and Disc priests fully HoT'd resto druids can be annoyingly difficult to kill (compared to Shamans who can purge & FS/LvB).
Having to drop form to heal can be painful too, and this problem gets compounded when you're being attacked by melee classes at the same time.
But the biggest drawback IMHO, apart from vulnerability AoE fears, is the lack of mitigation from incoming spell damage. Typhoon can be used as an interrupt if your opponent is in front of you (and in range), but your out of luck if the damage is coming from the sides or back. Compare this to shamans who have both an interrupt with Wind Shear and an immunity in grounding totems

Don't get me wrong - I love playing my druid team, and for BG's and WG they are a blast! But when playing them I have to be very mindful of their weaknesses too. They are very much a 'run and gun' play style - there's a lot of runing to a spot, pew pew, run to another spot, pew pew, et, while waiting for Starfall and Treants to come off cooldown. Compared to the 'turret defense' style of shamans where there's more of picking a spot and nuking anything in range.

Hope this helps...

Cheers,
S.