This is at once the problem with and the excellence of shamans in raids. What they bring is often most clearly seen in specific encounters like the Fathom-Lord, where their particular class abilities can be most clearly taken advantage of. It's difficult to enumerate all the ways shamans can contribute, since there are often new ways being discovered and taken advantage of by good raid leaders and skilled shaman players. Whether it's interrupting the mind control being channeled onto a tank, helping with emergency mana generation for a caster group, healing multiple melee at once, putting a great deal of damage onto a mob while buffing the DPS, dropping fire elemental totems to help gather up the murlocs... my recent forays into T5 content (in my blue gear, no less - the shoulders and legs I'm wearing in the picture accompanying the article literally dropped last night, before that I was tanking Al'ar in blues and greens...and being kept alive by a shaman, no less) have shown me that often, we will be using a shaman in a variety of roles, slotting them into whatever need a particular fight highlights.
In essence, the shaman becomes a showcase player, trying to answer a particular curve ball the encounter presents. Does the mob apply a nasty poison to the tank (I'm looking at you, Romulo)? Then a poison cleansing totem is utilized. Does the mob repeatedly heal herself or another (Julianne)? Then you can expect to see some earth shocking. I've been used as healing, as DPS and even as a weird form of kite tank in the Opera event, depending on what particular bosses we get. I admit I like using flame shock on the scarecrow especially since I'm in mail and wearing a shield, so I take less damage from him. Unfortunately, flametongue doesn't seem to make any difference on him.
It's my opinion, not only as a shaman but as a tank, that shamans get better and deliver more to a 10 man raid than they do a 5 man instance run, and even more to a 25 man raid, their particular strengths multiplying when supporting a larger group. Having three or four shamans in a 25 man raid means you can spread those totem buffs out to more people and tailor which players get which totems: a melee DPS group with warriors, rogues and an enhancement shaman can become a whirling engine of death with totem buffs and Unleashed Rage while a caster DPS group will love the buffs an elemental shaman brings. As I mentioned before when talking about the Fathom-Lord fight, you can also tailor a group to take care of an annoying add like the priest and having an elemental shaman in that group helps immensely. For some encounters, it's actually a good idea to put a resto and elemental shaman in the same group as their totems can help buff each other as well as you. If, for instance, you have the elemental shaman dropping totem of wrath and wrath of air, the restoration shaman can give you windfury, and since one of them will probably drop mana spring the other can drop healing stream. I know that a lot of shamans decry Stoneskin as useless but I've found it very useful when having to tank multiple mobs and I like when I can have it alongside strength of earth.
The reason the larger 10 and 25 man groups can really allow shamans to shine is because CC is much less important there, in my opinion. There's going to be rogues, hunters, mages and warlocks available to do that kind of thing, and the lack of competition fostered by the limitations of a 5 man instance run (especially in a PuG, when people don't know each other and are far less willing to trust each other's competence, leading to scenarios where groups either want as much CC as they can possibly get or want a tank who can grab and hold four or five mobs indefinitely) means that shamans get to show off their strengths instead of being penalized for the things they can't do. Furthermore, the particular power of shaman totems is their ability to provide group-wide buffs tailored to specific situations (caster buffs, resistance buffs, melee damage buffs, several direct or AoE damage options) gets stronger when more people can take advantage of them. When fifteen or twenty members of the raid can be buffed in this fashion based on what those particular players can themselves do, the effect benefits from this synergy.
All of this is in addition to their own impressive abilities. Restoration shamans are very effective splash healers, being able to use chain heal in addition to the ancestral healing buff to help keep a large group of melee DPS upright, especially if they're quick on knowing when to use rank one Healing Wave to help get Healing Way stacked on people. Elemental shamans can put out some really astonishing DPS while making every other caster avoid resists and crit more often (try one with a moonkin, I promise you it's an excellent combination) and are usually a bit less squishy than other casters, which is nice for when they pull aggro. Likewise, enhancement shamans are excellent physical DPS, although they often deliberately lower their own damage by dropping a Windfury toetm instead of Grace of Air, which would boost their own crit rate. (Windfury totem doesn't do anything for a enhancement shaman who is most likely using his own, superior Windfury weapon imbue). Last night, however, we had a shammy dropping grace of air for the main tank, who needed the mitigation more than the aggro generation of WF in case the murlocs got on him for a few seconds and ate up his shield blocks.
It's not just about shamans as swiss army knives or emergency assists: they can contribute substantially in the roles they've chosen and specced for. I don't think it can or should be forgotten, however, that of all the 'hybrids' shamans are the closest thing to a true support class in the game. No matter their spec or role, a shaman makes the raid better, not always through their own direct damage or healing but through the variety of tools they can provide to an encounter and the damage and healing they can help others perform. Having finally gotten a chance to really raid as one and alongside them, I wouldn't want to do without them.
Shamans are awesome. What do shamans do in raids? Almost everything. What's more, what they really do in raids is make you a better raider. Are they perfect? No, there are and will always be issues, but for the most part, I'm ecstatic to play one and always happy to have them come along.