I've played up to level 19 as a SS (Sith Sorc) and up to 12 as an IO (Imperial Operative). I have not tried Merc yet, which is the only other healing class I haven't played. The classes on different factions are mirror images in terms of the function of their abilites, although story wise they are different (Think Heroism vrs Bloodlust). So, a Sith Sorc is basically the same as a Jedi Sage.
In general, the Holy Trinity (Tank-Healer-DPS) is alive and well in the old republic, and general chat is alight with the calls of "looking for healer/tank for...."
The healing stat is called Presence and it increases the amount of healing you do for all classes. In addition to this, it also happens to increase the amount of health and damage your companions do. Every class gets companions although they vary from class to class. The net result of this is that when soloing you can use your companion to tank and/or dps thanks to your presence bonus, and when grouping you can rely on your groupmates. At least up to level 19, its perfectly viable to solo as a healer, thanks to this.
There are a LOT of group quests in SWTOR so its not hard to find work, unfortunitely there are few 'instances' as they exist in Wow. Considering the one that I have played is amazingly good, I'm hoping more get added. Some group quests have mini-instances.
Max party size is 4, so a typical party is tank, healer and 2 dps, but no one has tanking or healing abilites before level 10, so its pretty much a dps race until then. It stays like that until around 15 then it starts cranking up quickly. By 19 doing most group content was impossible without a healer and really hard without a tank.
For class specifics, I'll start with SS. You begin as a SI, which has no healing ability. You recieve your first heal at level 10 when you pick Sith Sorc. Your other option is Sith Assassin, however they cannot heal.
SSs have a force pool of 500 points. This is set and cannot be increased by stats. There may be talents to increase it, sort of like how rogues can get 120 energy. Its sort of a hybrid between energy and mana. Presence increases a SS's force regeneration, and being that its the same stat that increases raw healing output, its kind of important to prioritise it over everything else. Force regen for SSs does seem much slower then other classes, but it may just be that they have a bigger pool so it seems smaller.
In tough fights, especally when we had no tank, we wiped once I ran out of force. This was typically because we took so much damage I was forced to spam heals. When we had a good group with a tank, I did fine and could even throw some damage dealing spells into the mix. Healing a dps vrs healing a tank is very noticable, like in wow.
SS's also have a very nice CC ability called force whirlwind which works on anything other then bosses and lasts 60 seconds or until an idiot in your group breaks it. It has a 60 second cooldown, so if it is broken, your SOL because you can't reapply it. Compainions are intelligent and will not attack enemies you've CC'd and will stop attacking if you CC them during combat. Groupmates on the other hand, may vary.
SSs are sort of a mix between priest/mage/warlock as far as Wow comparisons go. As of level 19 I have a 3.0 (2.5 with talents) big heal thats force-efficent, a 1.5 second small heal that burns force quickly, and a shield that is basically PW:S down to the debuff that prevents it from being reapplied. At level 20, there is a talent that is an activated ability that is a direct heal + heal over time. From looking at the tree, eventually SSs also get an in combat ress, a threat reduction mechanic (Fade), and even a lifegrip ability that also reduces threat on the target.
Offensively, SSs have Force Lightning, which acts like mindflay, channeled damage with a 50% snare, plus a full complement of dots, direct damage, and AOE. The offensive damage stat is called willpower for force users. As it is a seperate stat, you'll have to keep 2 sets of equipment if you don't want to rely on a group or your companion for dps.
The downside to the SS is a lack of zero cost ranged attack. All your ranged attacks cost force, so if your saving all your force for healing, you either stand around doing nothing when no one needs a heal, or run into melee to wack things with your lightsabre using your regular attack, which does pitiful damage. There is no 'wand' option.
The other healing class I tried is the Imperial Operative. They begin as Imperial Agents and recieve their first heal at 10. The other option is Sniper, which cannot heal.
Interestingly, Imperial Operatives can stealth. A stealth healer holds a certain appeal to me but I've only gotten up to level 12 and haven't pvped on the character yet so I'm not sure how well it works in practice.
IOs have a pool of 100 energy that regenerates quickly, like a rogue. A healer with an energy mechanic is very interesting in theory but I haven't checked how it works in practice. Again, I'm only level 12 so right now there isn't much challenging group content.
The first companion you get as an IO is a ranged DPSer, which isn't as useful as the SS's tank companinion, but does do a lot more damage. IOs also have a CC called Slice, but it only works against droids. Otherwise its exactly the same.
As with all healers, Presence is the stat that increases healing for IOs, and it also increases companion damage and hp. Base ranged damage is calculated by Aim (its like strength, but for blasters) and 'tech' damage is calculated by Cunning (its like willpower, but for non-force users)
As far as heals go, as of level 12 I have 2. The first you recieve at level 10 and is a 3.0 second (2.5 with talent) big energy efficent heal. (You shoot a Kolto injection dart at an ally, which is pretty cool) The second is much more interesting, its a 3 second channeled heal over time with low throughput but is completely free. No energy cost, no cooldown. This is a fascinating idea, its basically like a healing auto-attack. Ideally this would be weaved in with stronger heals. At level 20 there is a talent for an instant cast HoT (Renew), there is also a 1.5 second heal at higher levels, which oddly has a 20 second cooldown.
IOs use blaster rifles, so you have plenty of ranged attack options including a variety of grenades (frag, incendary, flashbang) and gagets. Interestingly, they also have a few melee abilites including a backstab to complement their cloaking ability.
IOs can also use the cover system which in theory allows you to hide behind certain objects and use them for cover. In practice at level 8 you recieve the ability to create a cover point with a portable forcefield so you'll never bother with trying to find a preset one ever again. The ability is free and the only limiting factor is a 6 second cooldown.
The good thing about cover, as far as healing goes, is while your in cover and not attacking or using abilites, there is a high chance for ranged attacks to miss you. I don't think the exact chance is documented anywhere but it seemed to be fairly high. In theory it should help if you pull agro from a ranged mob the tank didn't pick up. There are also some abilites which can only be used from cover, although at the moment the only one I have is Snipe, a big damage big casttime nuke. I don't think any heals require cover, and I suspect cover is more important to snipers then to operatives.
Not much I can say about them in practice as I only ran the first instance with one in a group, and its easy enough that a healer wasn't really required. I plan to get the character to around 20ish and then try Mercenary.
The last healing class, which I haven't played yet is Mercenary which starts out as Bounty Hunter. The other choice is Powertech, which cannot heal.
They use a Heat system which could be described as a reverse energy system. They have a meter that starts at 0 and goes up to 100, each ability has a heat cost and cannot be used if doing so would exceede 100 heat. Heat reduces with time, much like energy regenerates. Merc's can't use cover like IOs can and use dual pistols instead of rifles.
I'm not sure what their abilites are, but they definitely have a healing talent tree like IO and SS does.
Thats the skinny on healing in KOTOR. If you have any other questions feel free to ask and I'll try to answer. If any other healers with more experience want to chime in too, thats fine. I've only been playing since Saturday.