There are 10 classes in the game. You can choose from 4 of them (Swordsman, Berserker, Hunter, or Druid) for your main character; your companions come from all 10 classes.
Your main class is chosen when you first start the game, before you have any idea what you're doing, and affects everything you do from then on. (Of course you can always reroll, or start a new character when the next server opens…) There are endless debates about which class is overpowered at the high levels, which you can read on the forums if you're interested.
Focused on defensive tanking; comps tend to have defensive skills (e.g., Neil's skill doubles his phys and mag def and heals him). They make great tanks, but wasting a space for someone who neither hurts the enemy nor heals your team is usually not worth doing.
Specializations: Phy Atk, Phy Def, Skl Def, Mag Def, Block, HP.
Balanced between (physical and skill) offense and defense. Comps often have skills with side effects (e.g., Calvert's can stun a row). Make good tanks, especially if you get them some decent counter.
Specializations: Phy Atk, Phy Def, Skl Def, Block, Resilience, HP.
Pure physical attack and countering. Skill attack is generally terrible, but side effects may be useful (e.g., Kelvin's increases his Critical and Hit). May be worth putting on the front line just to counter.
Specializations: Phy Atk, Skl Def, Counter, Hit, Critical, HP.
Magic attack, with a secondary focus on skill attack—pure damage, no side effects. Generally very fragile. But if you can keep them alive, many enemies (especially PvP) have low magic defense, and magic can't be dodged.
Specializations: Mag Atk, Phy Def, Skl Atk, Skl Def, Critical, HP.
Hunters focus on pure skill attack, primarily for damage rather than side-effects. Although their physical attack isn't usually as bad as monks', it's rarely anything exciting. While they're very fragile (even more so than monks), they can be built to dodge most hits, which can be even better than taking them and surviving (although this makes them weak to magic, which can't be dodged).
Specializations: Phy Atk, Skl Atk, Phy Def, Critical, Dodge, HP.
Assassins trade in their defense and hp for heavy critical hits. Their critical and lethal are their weapons and are easily capable of one-shotting enemies. Most of them also have the ability to strike behind guardians, use control effects like charm, or otherwise wreak havoc with the opponent's carefully-planned formation.
Specializations: Phy Atk, Skl Atk, Phy Def, Critical, Lethal, HP.
Monks are focused purely on skill attack, both damage and side effects (DoT, tranq, control effects, etc.). Some of them can be decent tanks (like Andre); others are pure glass cannons like (Ying Chen), and once their skill attack has gone off their value to the team is done.
Specializations: Phy Atk, Skl Atk, Critical, Pierce, Hit, HP.
Healers. Other than Luna, their heal is a fixed amount, which quickly becomes obsolete, but you may want to keep them around for side effects (Lulu's +rage) and/or as tanks.
Specializations: Phy Def, Skl Def, Mag Def, Block, Resilience.
Magic attack, with a secondary focus on skill attack and side effects. Less fragile than mages; some can tank, and all can dodge.
Specializations: Mag Atk, Skl Atk, Skl Def, Phy Def, Dodge, HP.
Each one is different, but generally a cross between a Farseer and a Priest.
Specializations: Phy Atk, Skl Atk, Skl Def, Mag Def, Resilience, HP.