There are 9 classes World of Wacraft offers you, varying on which race you pick, such as only Night elves and Tauren can be druids.
Warrior - The main class, all races can play as a Warrior. Warriors are damage dealers/damage takers, they have heavy armour and weaponry from the very start. Warriors role in activities is usually to take attention of the target creature, and make it center on the warrior so casters can use spells on it. This is known as "tanking", and warriors will usually be asked to do this. Fun, simple and powerful - warriors are for the people who like good action.
Mage - Mages cast spells of Fire, Ice and Arcane. Doing heavy damage, further than that of a warrior, mages are support for tanks and are counted on to do heavy damage and crowd control. Although, this strength comes at a loss. Mages wear weak cloth armour and cannot survive for long in combat, meaning that skill is required to play this class. Mages are the primary magic class (i say this because they are pure magic, no melee).
Rogue - The fastest striking class. At low levels, they learn how to use dual weapons, giving a huge increase and speed. Based on stealth attacks and high speeds, rogues make a great Player versus Player class, and are usually sen in battlegrounds taking out the bulk of enemies. They have alot of special attacks that increase strength for certain attacks, take damage down overtime, and finishing moves that require "combo points" which are gained by using special abilities. Rogues are a popular and powerful class, very popular and fun to play.
Druid - Druids are shapeshifters and only 2 races can play as them, the Tauren and the Night elf. Druids are in touch with nature and can take on the form of a bear, a cat, a seal and a cheetah. Bear is similar to playing warrior - you can take alot of hits and deal heavy damage. Cat is like playing rogue, stealth and speed. Seal and Cheetah give a speed bonus, seal gives a swim bonus and cheetah gives a land bonus. Druid in normal, biped form use destructive nature spells and healing spells. Druid is a very fun class to play, but not popular due to Blizzard giving them mainly healing items.
A Female Night Elf Druid
Warlock - These are like an evil mage, alot of spells that do quite a lot damage, and overtime damage. They also have the ability of summoning demons to aid them, such as the imp, who is a small demon who will throw fireballs at your target while you hit it with spells, or the Voidwalker, who is a black shadow-like demon which takes the attention of your enemy so it will not attack you, and you can hit it with you spells and not get bothered, unless the voidwalker is killed. Again, very fun to play, but for patient people.
A Female Human Warlock with Felhunter demon pet
Paladin - Holy warriors of good damage and armour, they are a tank that use spells to aid them aswell. They use the same kind of equipment as warriors, heavy armour and weaponry, but do not use the damage boosting abilities. They use healing spells and smiting spells to aid them. They have the third most powerful heals in the game, priests being the best, druids being the second best. They can ressurect, shield allies, and heal them back to full health. A very popular class only available to the alliance, and only 2 races of the alliance, dwarves and humans. People say leveling up is a complete drag, but well worth it in the end. Paladins are very powerful, but only for patient people.
Shaman - The horde equivalent of a Paladin, they use nature spells and healing spells, but arent as well armoured as Paladins. They use a good mix of elemental magic, melee fighting, and healing spells. Shamans are very powerful and popular, having some very powerful spells and the ability to summon totems which help them in battle. They are split into 4 elements, earth, fire, ice and wind. Earth is defense and support, disrupting spells to help them stop healers. Fire is offensive and strong, the totems will fire fireballs to help you. Ice is powerful and helpful, slowing the speed of your enemy. Wind is about speed, with great power. Shamans are a powerful class, and fun to play.
Priest - The primary and best healer class. Priests are relied on for the teams safety in the end, and are very important to a good group. With out a priest in major dungeons and instances, the team will not last long. Priests arent all about holy healing magic though, they can concentrate into a more dark "shadow magic" list of spells which cause damage and do major stat drops to armour and strength. Wearing weak armour and okay weaponry, priests are for the patient, quick thinking and people who dont mind watching action more than experiencing it close up.
Hunter - This class is one of the best Player vs Enviroment. They start off with a ranged weapon, such as a gun or bow, and get special abilities such as shooting poisonous rounds and arrows. Hunters wear medium armour, leather , so can take quite a bit of melee damage, and can use powerful weaponry and even learn to dual wield. Though, the most special thing about hunters, is the ability to go out and tame a wild animal to use as a pet who will help them fight monsters by taking the hits while you shoot. Hunters are very fun to play but the range of abilities are nothing special. So, fun, but for people who dont mind spending time getting meat or plants for their pet.