I'll start with some things I've observed and someone else can jump in to add/correct.
**Warrior** Usually if there's only one warrior, he'll be the designated tank. In the lower level instances, having maximum damage mitigation isn't as important (for a war) as being able to hold agro on multiple mobs at the same time. A warrior as a tank should keep an eye on all mobs in a pull. This way the warrior can go after mobs that make a mad dash for the casters. To keep agro on multiple mobs, the warrior will need to use various AoE skills in conjunction with large agro single target skills on the mob everyone is attacking (tactical mastery helps). Hamstring on runners helps when the group lacks other classes with good snares.
**Rogue** The lower level the instance, the more a rogue can be a tank (for one mob at a time). When the group already has a tank, the rogue helps with agro management by using feint to not get unneeded agro. Vanish/evasion can also be used in emergencies. A good rogue can be tough to kill and the healer can focus on other classes first. Sap will be useful as a form of CC. The rogue is a good class to be a main assist or a peeler.
**Mage** The mage is useful for dealing damage and having an excellent source of CC. A good mage will have a feel for how long his polymorphs last and be able to reapply polymorph before the mob has recovered. Mages can also get a feel to how much hate their spells generate so that the don't burst too much. Frost nova will sometimes help as a short-duration CC. Additionally mages can try to manage their mana (when beneficial) to be in line with the primary healer's mana such that as little downtime is needed. Some instances will require cure curse. In most high level instances, instant arcane explosion and improved counterspell will be VERY handy. Mages are a primary damage dealer and should use an assist macro.
**Priest** Priests will usually be designated as primary healers and sometimes that means not casting any damage spells in the pursuit of group efficiency. When possible, it's a good idea not to use HW: shield in combat as it appears to draw more hate then heals. Greater heals can be used on tanks with good armor while flash heals will be necessary on softer classes. People tend to get nervous when their health drops below 50% and depending on the instance it might be good to keep everyone above when possible. In certain instances, mind control and shackle can be used to great success.
**Hunter** Hunters bring a good amount of sustained DPS to the group while being relatively low-maintainence in the way of healing required. Their freeze trap can be useful as a form of short duration CC to an incoming mob or as a safety placed on the healer for the beginning of the fight. They can feign death to remove agro from themselves and use their pets to taunt mobs off casters. Hunters can also be on the lookout for patrols on the minimap with tracking. Hunters are a primary damage dealer and should use an assist macro.
**Warlock** The warlock is sort of a magic niche-filler. The imp group stamina buff is appreciated and it does pretty decent damage for a pet. The succubus can offer CC through mesmerize. The voidwalker can be used as CC to keep a mob busy at the beginning of a fight. The felstalker can eat up magical debuffs or monster buffs. The warlock himself has banish which is a useful form of CC in some situations. A good warlock will know which monsters will run away on low health and apply Curse of Recklessness (rank 1) to them. A warlock also can place soulstone on a rezzer and provide healthstones to the main tank and/or mage (who's using AoE). Warlocks have decent AoE options and alliance ones can cast uninterruptible (with the help of a paladin and talents). The warlock should use an assist macro before placing any DoTs on a target.
**Druid** The druid is an all-around niche-filler. However, in the higher levels the druid will need the right gear or talents to fill in different roles. A feral druid with good armor and stamina can tank well in bear form. A restoration druid with decent int and spi can heal well enough to be a primary healer. Cat form is underpowered in the higher levels and not as useful to use. The druid may be called on to act as group healer in the higher level instances because of a general lack of priests. A good druid will change into bear when he gets a lot of agro at once (possibly cheetah in Zul'Farrak). Regrowth spam may be required to heal mages that are bursting with Arcane Explosion. Healing touch can be used on tanks and it might be a good idea to hotkey two different ranks of the spell. Cure curse and poison will be necessary in some instances along with entangle and hibernate.
**Paladin** The paladin is a good buffer and will need to pay attention to when blessings drop. Playing a paladin well requires pre-battle thought to which blessings and seals would be most beneficial to use against the coming fights. They can offer some in the way of emergency or touch-up healing. A paladin can be the safety for the group by casting blessing of protection to save a caster from death or divine intervention to same the group from a corpse run. Cleanse will be very useful in many instances. The paladin should use an assist macro for when he melees.
**Shaman** not enough first-hand observations/experience with high level instances.
Edit: Druids cure poison and not disease.
**Warrior** Usually if there's only one warrior, he'll be the designated tank. In the lower level instances, having maximum damage mitigation isn't as important (for a war) as being able to hold agro on multiple mobs at the same time. A warrior as a tank should keep an eye on all mobs in a pull. This way the warrior can go after mobs that make a mad dash for the casters. To keep agro on multiple mobs, the warrior will need to use various AoE skills in conjunction with large agro single target skills on the mob everyone is attacking (tactical mastery helps). Hamstring on runners helps when the group lacks other classes with good snares.
**Rogue** The lower level the instance, the more a rogue can be a tank (for one mob at a time). When the group already has a tank, the rogue helps with agro management by using feint to not get unneeded agro. Vanish/evasion can also be used in emergencies. A good rogue can be tough to kill and the healer can focus on other classes first. Sap will be useful as a form of CC. The rogue is a good class to be a main assist or a peeler.
**Mage** The mage is useful for dealing damage and having an excellent source of CC. A good mage will have a feel for how long his polymorphs last and be able to reapply polymorph before the mob has recovered. Mages can also get a feel to how much hate their spells generate so that the don't burst too much. Frost nova will sometimes help as a short-duration CC. Additionally mages can try to manage their mana (when beneficial) to be in line with the primary healer's mana such that as little downtime is needed. Some instances will require cure curse. In most high level instances, instant arcane explosion and improved counterspell will be VERY handy. Mages are a primary damage dealer and should use an assist macro.
**Priest** Priests will usually be designated as primary healers and sometimes that means not casting any damage spells in the pursuit of group efficiency. When possible, it's a good idea not to use HW: shield in combat as it appears to draw more hate then heals. Greater heals can be used on tanks with good armor while flash heals will be necessary on softer classes. People tend to get nervous when their health drops below 50% and depending on the instance it might be good to keep everyone above when possible. In certain instances, mind control and shackle can be used to great success.
**Hunter** Hunters bring a good amount of sustained DPS to the group while being relatively low-maintainence in the way of healing required. Their freeze trap can be useful as a form of short duration CC to an incoming mob or as a safety placed on the healer for the beginning of the fight. They can feign death to remove agro from themselves and use their pets to taunt mobs off casters. Hunters can also be on the lookout for patrols on the minimap with tracking. Hunters are a primary damage dealer and should use an assist macro.
**Warlock** The warlock is sort of a magic niche-filler. The imp group stamina buff is appreciated and it does pretty decent damage for a pet. The succubus can offer CC through mesmerize. The voidwalker can be used as CC to keep a mob busy at the beginning of a fight. The felstalker can eat up magical debuffs or monster buffs. The warlock himself has banish which is a useful form of CC in some situations. A good warlock will know which monsters will run away on low health and apply Curse of Recklessness (rank 1) to them. A warlock also can place soulstone on a rezzer and provide healthstones to the main tank and/or mage (who's using AoE). Warlocks have decent AoE options and alliance ones can cast uninterruptible (with the help of a paladin and talents). The warlock should use an assist macro before placing any DoTs on a target.
**Druid** The druid is an all-around niche-filler. However, in the higher levels the druid will need the right gear or talents to fill in different roles. A feral druid with good armor and stamina can tank well in bear form. A restoration druid with decent int and spi can heal well enough to be a primary healer. Cat form is underpowered in the higher levels and not as useful to use. The druid may be called on to act as group healer in the higher level instances because of a general lack of priests. A good druid will change into bear when he gets a lot of agro at once (possibly cheetah in Zul'Farrak). Regrowth spam may be required to heal mages that are bursting with Arcane Explosion. Healing touch can be used on tanks and it might be a good idea to hotkey two different ranks of the spell. Cure curse and poison will be necessary in some instances along with entangle and hibernate.
**Paladin** The paladin is a good buffer and will need to pay attention to when blessings drop. Playing a paladin well requires pre-battle thought to which blessings and seals would be most beneficial to use against the coming fights. They can offer some in the way of emergency or touch-up healing. A paladin can be the safety for the group by casting blessing of protection to save a caster from death or divine intervention to same the group from a corpse run. Cleanse will be very useful in many instances. The paladin should use an assist macro for when he melees.
**Shaman** not enough first-hand observations/experience with high level instances.
Edit: Druids cure poison and not disease.