The most tried-and-true way to build an ideal group consists of the following Holy Trinity:

• Tank(s) to take the damage (Warrior, Druid, Paladin and Death Knight.)
• Healer(s) to keep party members alive (Priest, Druid, Shaman and Paladin.)
• Damage dealers to deal most of the damage (Mage, Warlock, Hunter and Rogue are pure damage dealers but all classes can be damage dealers as well with the right spec and gear.)

Having each of them covered is not the only way to survive, but many people will initially try to build such a group when setting out for instance runs at high levels.