Totems! Totems! Totems!

The biggest advantage (and biggest pain) of the shaman class is the incredible buffs provided by their totems. The downsides to these great buffs are a limit of one type per element, a lifespan of two minutes or less, and a limited range of 20 yards (30 with a Restoration talent). These make the buffs somewhat less flexible than shaman (and their raidmates) might like, but they're still very valuable nonetheless.

I'll quickly run down the four elements (remember that you can only have one out of each element) and provide comments on each. Benefits listed assume non-talented, max rank totem.

Air
Of all the elements, Air has the greatest collection of useful totems. Sadly, you're limited to one.

• Grace of Air: Hunters and feral druids will love you for the extra 77 Agility provided by this totem. It's also useful for providing additional damage mitigation to your tanks and a little bit of melee crit as well.
• Grounding: A great situational tool, Grounding Totems "eats" one single-target spell. It can occasionally grab two if they were cast simultaneously and non-damaging effects like Cyclone won't consume the Totem. It's one of the best totems for PvP, but can also be useful for some raid bosses (Maiden of Virtue in Karazhan, for example).
• Nature Resistance: Useful for when you don't have a hunter in your group, it provides an additional 70 NR. Does not stack with Mark/Gift of the Wild or Aspect of the Wild.
• Sentry: One of those "Huh?" kind of totems, it allows you to view the area the totem's in for 5 minutes. Potentially useful in battlegrounds, I guess.
• Tranquil Air: Reduces threat by 20%, which does stack with the paladin's Blessing of Sanctuary Salvation. Obviously of little use in 5-man or in a tank group, it can be helpful to drop at the beginning of boss fights to keep your party from pulling initial aggro due to an unlucky crit string. For truly threat-limited characters, this may also provide a bigger cushion.
• Windfury: By far the best totem in the game, Windfury grants a 20% chance for a second attack with main-hand weapons. This totem can improve a DPS warriors damage output by as much as 20%! Rogues can also see similar results, especially with a sword spec. It's also great for helping your tank generate rage (and therefore threat) faster. This totem is important enough to warrant additional discussion:
  
  
  • The WF buff is only available if no additional buffs are on the weapon (mana oils, sharpening stones, poisons, etc.). So make sure your rogues click off their main-hand poisons beforehand (all classes of rogues benefit more from WF than from poison).
  • The WF effect is applied as a 10s buff. This makes it possible to "twist" totems, to grant both Windfury and Grace of Air by casting WF, letting it pulse, and casting Grace, repeating this every time the WF effect wears off. Although this gives an additional boost to your melee, it's generally regarded as a waste of mana and your global cooldown, so don't bother.
  • The shaman's WF effect is significantly better than WF totem plus another weapon buff (Rockbiter, Flametongue, etc.). Always go with the WF buff and use the totem only when grouped.
  • WF? Or GoA?: If there is a DPS warrior in your group, use WF. If there are 2 or more rogues in your group, use WF. If your tank doesn't need the additional mitigation, use WF. If you have hunters/druids (and no warriors and 0-1 rogues), use GoA.
• Windwall: This totem is not very useful, reducing ranged damage by 102. Occasionally useful when taking ranged fire from multiple sources (the AV towers, for example).
• Wrath of Air: A favorite of casters and healers, this increases healing and spell damage by up to 101. The improvement is generally less than melee receive from WF or GoA, so if in a mixed group, generally go with the melee totems.

Earth
Earth also has a wide variety of totems, including one of the two elementals.

• Earthbind: Primarily a PvP totem, it slows enemies down. Its effect is pulse-based, unfortunately, so it doesn't always kick in before your enemy gets out of range.
• Stoneclaw: A pretty weak totem, it casts a small-range AoE taunt and stuns enemies that attack it. Pretty much useless for raiders (both because many mobs are immune and can easily one-shot the totem, even with its 1315 health), it has occasional uses in PvP (pulling pets off of you, for example) and soloing (to allow you to get away).
• Stoneskin: Another weak totem, it reduces melee damage by 43. The amount is miniscule in a raid setting, so is really only useful in occasional solo situations (fighting fast-hitting, relatively weak mobs, for example).
• Strength of Earth: One of the totems you'll be dropping frequently when you're in a melee group, it grants 86 Strength. In addition to the added bit of Attack Power, this is also useful to your tanks to increase their blocking ability.
• Tremor: Tremor totems remove Fear, Charm and Sleep from your party. It's also on a pulse system, so depending on when the effect kicks in, it's possible to run out of range of the totem. It's still a very useful totem, however, since most of the time it ends these effects much earlier. Obviously a great totem for PvP, especially when facing priests, warriors or warlocks.
• Earth Elemental: Summoning the Earth Elemental requires a totem as well, so be careful not to accidentally overwrite it with another totem. The elemental has a fairly strong taunt ability, but doesn't survive long against a raid boss. It's more useful when overwhelmed while soloing or for creating a little extra havoc in PvP (especially around flags). Be careful of using it in fights requiring crowd control as you do not get to control who it attacks.

Fire
Fire is probably the least-used group of totems for Restoration and Enhancement shaman, but is a favorite of Elemental.

• Fire Nova: Takes 5 seconds to "arm" before casting an AoE fire blast. It creates a small aggro pulse before arming, so if fighting multiple mobs, there's a good chance that one of them will hit the totem before it goes off. It can be used to good effectiveness in PvP often times.
• Flametongue: Provides an additional 20-60 fire damage to all weapon attacks. This is an inferior buff for melee, but is affected by +spell damage, so can occasionally be better for casters. For those few times they melee, anyhow....
• Frost Resistance: Provides 70 FrR. Does not stack with Mark/Gift of the Wild.
• Magma: Creates a pulsing AoE effect, which can be useful against large packs of mobs.
• Searing: Shoots fireballs at your enemies. With enough +spell damage, this totem can actually provide a pretty significant boost to DPS, although it can occasionally break crowd control, so use with caution.
• Totem of Wrath: The Elemental 41-talent, it provides +3% hit and +3% crit to the party. Many caster groups are built around this totem. Generally, this talent will do you more good than casting Searing totem for additional DPS, but is significantly better once you add in another player.
• Fire Elemental: This elemental has a decent DPS output (both AoE and single-target), but is fairly squishy. Be careful of using it in fights requiring crowd control as you do not get to control who it attacks, and the AoE will often break CC.

Water
Along with Air, Water is the most commonly used raid totem.

• Disease Cleansing: Instantly removes one disease effect from all party members and then on a pulse basis. More mana efficient than Cure Disease if you have more than one party member affected.
• Fire Resistance: Provides 70 FR. Does not stack with Mark/Gift of the Wild of paladin FR aura.
• Healing Stream: Heals party members for 18 every 2 second, but is improved with +healing. It can be very useful for combating regular, low-level AoE effects. In general, however, you will heal more from the extra mana from Mana Spring than Healing Stream will heal.
• Mana Spring: Another caster favorite, it restores 12 mana every 2 seconds (20 mana/2 with patch 2.3). This should be the default totem for any Restoration or Elemental shaman.
• Mana Tide: The Restoration 31-point talent restores 24% of all party member's mana over 12 seconds, but on a 5-minute cooldown. This can be a huge boost for healer or caster groups.
• Poison Cleansing: Similar to Disease Cleansing, only for poisons. Very useful against rogues in PvP.

So what should I drop?
In general always drop Mana Spring for your own mana regeneration (Enhancement may not want to bother, however). Also drop specialty totems depending on the fight (resistances, poison/disease cleansing, etc.)

Melee/tank group: Windfury or Grace of Air (see the WF discussion above) + Strength of Earth

Caster/healer group: Wrath of Air + Mana Spring (+ Totem of Wrath)

PvP: Grounding + Tremor. Depending on your group/arena makeup and your opponent's classes, Windfury or Wrath of Air may be more appropriate.