Although it's highly recommendable to complete any quest at low levels, as the experience gained is usually worth it ( u have to grind those mobs anyway, why not gain some extra experience while doing it?) there are some quests which either should be done at high levels or , for the patient ones, completed as any other quest with the sole remark that the reward is not to be used at low levels if the benefit is a percent of some kind and not an absolute value added. You will understand this by looking at the quests i selected:
1. The Alliance "Selling Fish" started by Dockmaster Baren in Redridge Mountains, available at level 16. The reward includes 5 x Fishliver Oil, which might be almost useless to a level 20 rogue, but very useful in certain situations (pvp, instances, world bosses etc.) for a higher level character.
2. The horde quest "A Solvent Spirit", obtained at level 5 in Durotar, from Master Vornal in Sen'Jin Village has the awesome reward which consists of 10 x Really Sticky Glue, excellent for the classes which can't trap a running foe. My rogue used it successfully in pvp either for catching a mounted enemy trying to run away either for escaping from one when the situation got out of hand. When the 10 charges where all used i even bought more from the low levels, but that was in the happy days before this item became BoP....:)
3. "Gold Dust Exchange" is a quest for Alliance only and it can be obtained at level 4 from Remy "Two Times" in Goldshire, Elwyn Forest. The reward is a Bag of Marbles with 10 charges. Imagine what this item would do against a opposite faction warrior or rogue :)
4. For the hordies willing to make a trip to Tirisfal Glades, Apothecary Johaan in Brill gives the quest "A New Plague" which rewards 5 x Slumber Sand, useful for those classes without any crowd control abilities or simply for those who can't use them against particular enemies ( for example, a mage fighting 2 demons might want one asleep, or when fighting a battle on the edge, the 20 seconds of sleep would be a nice chance to bandage if the frost nova failed etc.)