Quest rewards are often a thing of torture. You've gone out and collected all of
the required bear skins and elf heads to finally obtain the reward. The reward
is sometimes gratuitous giving you only gold or potions. Sometimes though it
gives you a multiple choice of items. These items then taunt you. Which one
should you choose? Sometimes you're lucky and there is only one thing you can
wear. Sometimes though you're given multiple useful items and choosing can be a
tough thing to do.
Rewards for quests can vary. Most quests before you hit the level cap will grant experience as a reward (although not all quests grant experience). Along with experience most quests also grant a variety of rewards. Most of the time these rewards are in the form of items, mostly armor and weapons. Then, most quests also grant reputation if they're given to you by an NPC of a notable faction. Rewards can also be in the form of reputation only, honor, or unlocking instances.
The difficulty in choosing the reward will often come when you're faced with multiple choices that fit your character. Some items are obviously not going to work because you can't equip them or their stats do not in anyway assist you. For instance, a Rogue can't equip Mail or Plate so those rewards are useless. A Rogue also can't really get much benefit out of spell damage and intellect so Cloth and Druid leather are out of the question. So obviously for the Rogue any kind of quest reward that grants Agility, Stamina, Attack Power, Critical Strike Chance, and any other melee orientated stats will be the best choice.
However, sometimes a situation will arise where it's not a question of what you can't equip. Sometimes you'll be given multiple rewards that all assist you in some way. Like some quests will give the option of choosing from three trinkets. Each trinket has a different gimmick effect that does something that is in no way related to your class. In this instance it's all about preference. Trinkets and rings are always easy to replace and even if you're at the maximum level you'll always find something better inside of an instance.
Then there are quests that give multiple weapon rewards. For casters this is generally easy since the staff is always going to win out (unless it's a Druid only staff) or caster one-hands. For classes like Warriors and Rogues then the question becomes what weapon to pick? Here you'll have to analyze which weapon would give you the biggest upgrade with your current setup. Consider how much weapon skill you currently have, if you'd have to skill up the new weapon, and how much of a benefit does it give you over your current stats. If it's not much of an improvement and would require skilling up then consider choosing a reward to sell off.
There are times (quite frequently I must add) where you'll find that there is no reward to choose that you can use. This is when the guessing game begins. The goal here is to choose the reward that'll sell for the most. Some use addons that supply item prices in-game, others look up the prices on the 'net, and then there is always the option of choosing items that generally sell for the most. Mail and Plate generally have the highest vendor price out of armor and any weapon is going to come with the highest vendor price. 2-handed weapons generally, from my experience, sell for the most. In Outland and beyond this can be a very difficult choice since the piece of cloth or the caster dagger may sell for 2 gold while that two-handed sword might sell for 14.
Whatever you choose remember that there are a almost no quest rewards that can be considered irreplaceable. Every piece of armor and every weapon will almost always have an upgrade from either another quest or from an instance. So even if you choose wrongly, click the wrong thing, or just don't pay attention and choose randomly you'll be fine.