Name: Serpent Sting
Description: Serpent Sting is a damaging shot that puts a nature DoT on the enemy that scales with AP. This is a nice, straightforward shot. Remember, as it is a DoT, it can prevent many forms of CC, including Freezing Trap, so be aware of that before you use it.
Use in PvE: Back before Burning Crusade, Serpent Sting had a place of honor in most shot rotations. These days, it's less used, since Beastmastery Hunters work with a 1:1 or 3:2 shot rotation and really don't have time to fit it in, and because it's not very mana efficient. Still, slower shot rotations should consider using it, at least in longer lasting battles where the DoT has some time to tick. If you're in a battle where you have to be on the move or kiting and your target won't be needing CC, this is some nice instant cast damage too, and probably worth squeezing off alongside Arcane Shot.
Use in PvP: If you're burning down a target, adding Serpent Sting to the mix may at least put the target down a little faster. Ace also reminded me that it's useful for keeping Rogues and Cat Form Druids from stealthing or vanishing, assuming Cloak of Shadows is down. In addition, in massed battle situations, you can quickly tab through many targets and put this up on them all in order to increase your damage potential and weaken the other side a decent amount. Again, however, be aware that this sting will prevent many forms of CC, so in some cases you may not want to use it for that reason.
Name: Viper Sting
Description: Viper Sting drains a good chunk of mana from the opponent over 8 seconds. Like all stings, its poison, so it can be cleansed. It has a 15 second cooldown, so you can't keep a target consistently drained. Despite the fact that it drains mana instead of health, it will still break forms of CC that break on damage, such as Freezing Trap. It also does not stack between multiple hunters.
Use in PvE: This shot has lost a bit of luster in PvE as of late. While it was useful against some raid bosses before Burning Crusade, such as Moam of AQ20, the need to mana drain really hasn't been a major boss mechanic since then, and even most normal spellcaster mobs have such large mana pools that you won't drain enough mana to prevent any spellcasts before they die, especially since the cooldown now prevents you from having it up all the time. Still, there is the odd mob here and there with a mana pool small enough to justify throwing out a drain, and if it takes you long enough to kill them, sometimes it's nice to have that mana drain up to prevent them from regenerating enough to cast another spell.
Use in PvP: PvP is where this sting really shines, mostly when used by drain teams, or when used against a single target to aggressively drain their mana, usually a healer. However, to use it effectively, you can't always just fire and forget it, especially not if you're up against anyone who can just cleanse it off. Specifically, you're going to want to stack poisons on their target so that they can't cleanse off the mana drain right away. There's two main ways to do this. The first is to bring along a scorpid pet. Their Scorpid Poison stacks up to 5 times, and each cast of Cleanse or each tick of Abolish Poison or a Poison Cleansing Totem will have a chance of cleansing one of those poison stacks instead of the Viper Sting. Similarly, you can try to lure your target into a Snake Trap, as the snakes' various poisons will also provide that extra buffer for Viper sting to work its magic.
Before Viper Sting had a cooldown, it was a popular trick for a Hunter to spam level 1 Viper Sting on a druid, paladin, or shaman over and over again, trying to trick them into wasting mana by cleansing it off over and over again. This isn't as useful a trick anymore since you can only use Viper Sting once every 15 seconds, but if you're in a drawn out battle and you're running low on mana, sometimes it may be worth it to try to use rank 1 Viper Sting as a fakeout.
Name: Scorpid Sting
Description: This sting will reduce the target's chance to hit with melee and ranged by 5% for 20 seconds. It does not stack between multiple hunters, so don't try to gang up on a target with it. Since it doesn't do damage, it won't break CC such as Freezing Trap. Thus, if you need to trap a target you've already hit with Viper or Serpent Sting, you can use this sting to quickly overwrite it before you lure the target into your trap.
Use in PvE: Most trash mobs will probably die too fast for this sting to of much use, but it can shine on boss fights. If your tank is having trouble with dying against a boss, consider weaving a Scorpid Sting into your shot rotation to give them a little relief, and possibly the edge you need to win the battle. Note that Gaeowyn the tanking rogue had a Hunter using this sting for many of his tanking victories. Unfortunately, as it is a poison, it won't work on poison immune bosses. It also doesn't affect spell hit, and thus might be less useful against targets that do most of their damage via spellcasting. Also, it will probably take away from your overall DPS since you'll need to disrupt your existing shot rotation to fit it in. Still, if it means the difference between a wipe and taking the boss down, it is well worth it.
Use in PvP: The main use for this in PvP is probably going to be the aforementioned clearing of CC-breaking stings, but if you or a teammate is having trouble shaking a melee attacker, it might be worth applying this sting to increase your survival chances until you can apply some CC.
Name: Wyvern Sting
Description: This sting will put an enemy to sleep for 12 seconds, then apply a poison damage DoT. It is a 31 point Survival tree talent though, so not every Hunter will have it. The DoT at the end can make this sting problematic for long term crowd control, although it can be overwritten with another sting, such as the aforementioned non-damaging Scorpid Sting.
Use in PvE: This can be useful for some quick emergency crowd control, or to put some distance between you and a kited mob if you're having trouble staying ahead of it. Just be aware of which mobs will be immune to poison or sleep, and thus to this sting. If you have a Freezing Trap break early, or break before your trap cooldown is up, you can use the Wyvern sting to buy some time. When you're ready to trap again, just use Scorpid Sting to remove Wyvern Sting (and thus the DoT), and lead the mob into your new trap.
Use in PvP: Generally, the uses for Wyvern Sting are more or less the same as they are in PvP -- you simply have to account for the extra smarts of a human-controlled target, as well as their ability to use poison cures, the PvP trinket, or even Stoneform to break it early. You could also feasibly use Wyvern Sting for an emergency spell interrupt in a pinch, or to keep a healer locked down just enough to burn down his DPS partner.
As a Hunter, just as with all classes, you should always have a firm grasp on your abilities so that you can be the best you can be, whether solo or grouped, whether in PvE or PvP. Stings are certainly a good part of a Hunter's usefulness. They are somewhat situational for the most part, but good use of stings is part of what seperates the Hunter from the huntard. Hopefully, you've learned a bit about how to use them, and have come up with some ideas of your own on how to fit them into your everyday play.