There are four base classes on each side (Republic vs. Empire, though we're talking old Republic and Sith Empire, several thousand years before the movies). Each base class has two possible advanced classes that you choose from at level 10. All the classes on each side are rough mirrors of each other, but differ in style and some abilities. For example, the Sith Inquisitor (primary force user) shoots lightning, while the Jedi Consular (Republic equivalent) hurls objects with telekinesis. Same outcome (ranged dps), different method.
Each advanced class has 3 talent trees, 2 unique to the class and one shared between both advanced classes. Each unique tree focuses on a role, while the shared tree offers general improvements to the class independent of role. The Jedi Sage (advanced class option for Jedi Consular), for example, has a dps tree, a healing tree, and a "balance" tree. The Jedi Shadow (the other option) has a dps tree, a tank tree, and the same "balance" tree. You can respec your talent trees, but as far as I know you cannot respec your advanced class choice.
Every class has some sort of group buff as a baseline ability, so having at least one of each base class in a group is going to be helpful. The group size is apparently 4, so having one of each base class is going to be ideal. If you have two of one class you won't be able to get all the buffs.
First a disclaimer -- the information that follows is based on my quick impressions over the beta weekend. It's not datamined information and some facts could be wrong, but it should be close enough for the most part.
Your basic lightsaber swinging Jedi. They specialize in melee attacks instead of force abilities, and are the clear "warrior" style archetype. The class mechanic is Focus. Some abilities generate focus, others use it. Starts with 0 focus and focus decays outside of combat. Early abilities include a couple of lightsaber strikes, a "leap into combat" ability, and a pbaoe.
- Jedi Guardian - The tank specialty. Fights with a single lightsaber, gets the ability to wear heavy armor, taunts, and a few iconic force powers like Force Push. Luke was probably a Jedi Guardian. Gets a tank tree and melee dps tree.
- Jedi Sentinel - The melee dps specialty. Fights with dual lightsabers, can wear medium armor, has a new mechanic in addition to focus called "concentration" that allows the use of special buffs. Gets a solo dps tree (survival + dps), or a group dps tree (pure dps). Or something like that. The Sentinel's role seems to be pure dps.
Precursor to the clone trooper and stormtrooper. Heavy ranged weapon class with the ability to wear heavy armor and use shield generators. The class mechanic is "energy cells". Abilities use a certain number of energy cells which recharge over time. There are some abilities to instantly recharge cells.
- Commando - The ranged dps specialty. Focuses on heavy weapon usage such as rocket launchers and massive blasters. Gets a dps tree and a healing tree.
- Vanguard - The ranged tank specialty. Focuses on shield generator usage and blaster rifles. Gets a ranged dps and a tank tree.
Heavy force using Jedi. Still gets a few lightsaber attacks, but they're pretty basic (still pretty effective though, at least at low level). Can only wear light armor. Mechanic is Force points (mana) but there's only 100 points, so it's more like an energy bar. Early abilities include a pbaoe + knockback and the ability to rip chunks of rock out of the ground and toss it at your target.
- Jedi Sage - Ranged force user. Focuses on force powers from range. Gets upgraded range on all the basic force powers (from 10m to 30m), an increase in Force points from 100 to 500, and learns advanced ranged force abilities. Gets a dps tree and a healing tree.
- Jedi Shadow - Melee force user. Focuses on force powers and stealth. Gets a stealth ability (affects your companion too!), a backstab, and a variety of force powers intended for use at short range. Gets a dps tree and a tank tree.
Han Solo. Well, it is. Mechanic is energy (like a rogue) with a secondary mechanic of "Cover". The Smuggler (and Imperial Agent) are the only classes smart enough to take cover when blaster bolts start flying. It's quite well done, your character literally crouches down behind appropriate world objects, and ranged attacks will hit the cover instead of your character. Enemies can flank you, or melee you to negate the cover bonus. Certain abilities can only be used from cover, and your character will pop out from cover to attack and then duck back down again. At higher levels the Smuggler can use a force field generator to create cover where none is otherwise available.
- Gunslinger - Range damage specialist. Can dual wield blaster pistols and focuses on damage. Gets a range dps/debuff tree, and an aoe/dot dps tree.
- Scoundrel - Support/close range specialist. Focuses on fighting from cover or supporting groups. Gets a short range/melee dps tree and a heal tree.
The Imperial classes are rough mirrors of the Republic ones, so I won't go into much detail, just list them. You'll have the basic idea based on the Republic equivalent.
Empire equivalent to the Jedi Knight. They fight with red lightsabers to let you know how different they are from those pansy Jedi.
- Sith Juggernaut - Tank specialty. Darth Vader was probably a Juggernaut. Gets a tank tree and a dps tree.
- Sith Marauder - DPS specialty, equivalent to the Sentinel.
Empire equivalent to the Trooper, but with more attitude. They also have a reverse mechanic to the Trooper. Where the Trooper starts with a full bar of energy cells, the BH uses "heat" which starts at 0. The Trooper depletes energy cells, and when he runs out can't use abilities. The BH generates heat, and when the bar fills up he can't use abilities. Same idea, but they work in opposite directions.
- Mercenary - Dual wield specialist, fights with dual blaster pistols. Has a dps tree and a healing tree.
- Powertech - Gadget specialist, has a dps tree and a tank tree. Think Boba Fett.
Empire equivalent of the Consular, they also believe in diplomacy first. Force Lightning is typically their start to negotiations.
- Sith Sorceror - The heavy force user, gets a dps tree and a healing tree.
- Sith Assassin - Stealth melee force user, gets a dps tree and a tanking tree.
Empire equivalent to the Smuggler, but quite a bit more martial in nature. Uses the same energy and cover mechanics.
- Sniper - Ranged dps specialty.
- Operative - Support specialist, gets a dps tree and a healing tree.
If you're counting, you'll note that each side has 3 classes that can heal, 3 classes that can tank, and everyone can dps, depending on how you spec. The most versatile base classes are the Trooper, Consular, Bounty Hunter, and Inquisitor, each of which have the ability to tank, heal, or dps (not in the same advanced class though). The Knights and Warriors can only tank or dps, and Smugglers and Agents can only heal or dps.
I think groups are going to be hard to form until they add in a dual spec ability, though even that might not change much. Companions mean you can solo with whatever build you like and it won't get much harder, you just use a different companion. It won't change the fact that many people don't want the responsibility of being a tank or healer -- it's stressful. I'm perfectly happy to tank or heal for a group of friends, but I despise doing it in pugs. I don't suck THAT bad, I just don't care for the pressure. Having just 2 slots for dps characters means they'll have even more trouble than usual finding groups. Hopefully low level content will be forgiving enough that a Jedi Guardian can tank even if he's specced for DPS, but we'll see.