Disc - ever since Blizz made our health pools huge relative to healing done, Disc has been amazing for progression. Absorbs really help against raidwide burst damage mechanics.
Holy Priest - Alas, Holy Priests are still a cross between a poor man's Resto Druid and a Disc Priest without absorbs. I think the idea is to be a throughput healer with more reliable burst. It just doesn't work out in practice very well, especially since Disc is OP. Until 5.2, there just isn't much justification to bring a Holy Priest.
Holy Pally - Their strength lies in Beacon of Light. This gives them a lot of efficiency while tank or triage healing.
Shaman - I'm not as familiar as Shaman, but they seem to do all their best work when the group is stacked up. They're like a Paladin with a bit more emphasis on group healing rather than single target.
Druid - Druids are stabilizers. They provide high throughput and can easily reach everyone in the raid. Great when there's constant damage on the whole raid.
Monk - Monks seem to have roughly the same strengths as a Druid, stabilizing throughput that isn't limited by spreading mechanics, and great when there's constant damage going out.
Disc Priest - they really need someone to back up their absorbs with real healing.
Holy Priest - They're best assigned to one role in the group based on their Chakra, and that usually works out to be raid healing. Their real weakness though, is triage.
Holy Pally - Needs the most help with healing spread out groups.
Shaman - Similar to Pallies, they seem to need help when the group is spread out.
Druid - Needs the most support when there's burst damage.
Monk - also needs a bit of support when there's burst damage.
Some comps seem to not work very well. It becomes clear what you should probably add as the 3rd healer to such comps (or what to avoid when 2 healing). Doubles of the same spec are obviously not ideal.
Disc/Holy Paladin: The Holy Pally has to concentrate too much on backing up the Disc Priest's absorbs, and/or the Disc concentrates too much on real healing instead of absorbs. Add: Druid or Monk.
Disc/Shaman: seems like it would be great while stacked, but might struggle a bit when the group spreads out. Add: Druid or Monk.
Disc and Druid/Monk: might struggle a little with tank healing, although Disc is a fine tank healer. Add: Hpally or Shaman.
Hpriest/Hpally - needs to watch out for mechanics that prevent one of the healers from healing, like MC's. Add: Druid, Monk, or possibly Shaman.
Hpriest/Druid/Monk - Probably need to put the Druid or Monk on the tank, so the Hpriest can stay in Sanctuary. Doesn't let the Druid/Monk concentrate on their strength. Add: Hpally or Shaman.
Hpally/Shaman - Probably pretty weak when the group spreads out. Add: Druid, Monk, possibly Holy Priest.