As the game develops and old content gets redone so does the class quests. Most often you can go back and do new ones with your high leveld toons even if you have done your old class quests. So, why do them? I’ll let Elishat and Tiny tell you why.
There are quests at lvl 20 that will give you a weapon.* And then there are the ones at lvl 50 that will give you a headgear that looks like tier 1 headgear for your class.* For some classes, such as mages and monks, there are other class quests as well that will reward gear.
Even if there are other ways to get the graphics of these items, these quests are most often the easiest way to obtain them. So my advice to you would be to walk by your class trainer to see if there are any class quests you have not done yet.
*Death Knights excluded.