Each class get specific quests that give you new abilities or class specific weapons. The following sections contains walkthroughs for each quest and advice on which rewards to take.
At level ten each of the races gain access to a simple quest that rewards you with a new weapon. The staff is usually the best choice since the orb requires a main hand weapon which is hard to find at your level.
Mirror Lake
If you are a human head to the mage tower in Stormwind and talk to Jennea Cannon. She needs you to gather a water sample from the waterfall outside of town. Take the flask she offers you and head outside the gate and south till you run into a river. Follow it upstream until you come to a large lake with a waterfall and fill the flask at its base. Return to the mage tower to turn in your quest and gain your reward.
Mage-Tastic Gizmo
If you are a gnome talk to Bink in the a Mystics ward to begin your quest. She left a certain magical item at her home in Gnomeregan and wants you to bring it back for her. Head out to western Dun Morohg and the entrance of Gnomeregan. Binks house is the two story hut just north of the entrance to the city. Look for a grey chest under a table and open it to get your item.
Control
If you are a Draenei head to Bati in the hall of lights inside the Exodar. She wants to test you by having you kill a Queldori Magewraith. To find one head north along the coast until you find a large group of siltfin murlocs. Kill them until one of them summons a magewraith. It hits very hard so if possible run away out of combat so you can eat and drink to full. When you are ready burn it down as fast as possible with fire spells. Once you have beaten it head back to Bati for your reward.
The Balnir Farmstead
If you are an undead talk to Anastasia Hartwell in the mage quarter of the Undercity. She needs to run some tests on the spread of the plague, and wants you to gather some samples for her. After accepting the quest east along the road from the Undercity to the Balnir Farmstead. The samples you need are the bushes inside the garden of the farmstead. After you have collected them head back to Anastasia for your reward.

Ju Ju heaps
If you are a troll head down to Sein'jin village and talk to Un'thuwa. The warlock Zalazane is causing havoc in the magical currents with several ju ju piles and Un'thuwa wants you to destroy them. Swim out to the echo isles and look for troll encampments. The ju ju piles are piles of skulls inside most of the huts and are usually guarded by an enemy troll. After destroying four return to Un'thuwa for your reward.
Recently Living
If you are a blood elf head to Instructor Antheol Just south of the Silvermoon Entrance. He will give you three different quests instead of one and the first has you retrieving a bottle from a nearby lake. The second quest has you take the bottle and gather water from a waterfall south of your location. There are several waterfalls along your way, but you will want the biggest one just west of Toriwatha. For your final task you will need to head back and get a Living Branch from one of the trents near the waterfall. After you have obtained one head back and turn it in to get your new weapon.
Robe Quest
At level 15 each faction of mages gain access to a quest for a new robe. For it's level it is actually quite nice and the extra EXP is a nice bonus as well so I highly recommend completing it.
If you are alliance head to Stormwind and talk to Jennea Cannon inside the mage tower. Your first task is to eliminate some arcane disturbances inside the Blue Recluse inn. Take the two coffers behind her and head down and a little north to find the inn. Once inside use the cantation of manifestation to make the monsters appear. They will link if you aren't careful so try to pull to a safe spot out of the way like the kitchen or upstairs. Attack one, and once you have almost killed it throw down a containment coffer to capture it. Repeat this process two more times and head back to Jennea.

Now it is time to make your robe. For this you will need 10 pieces of linen cloth which can be easily farmed. The other main ingredient is six charged rift gems. You will find these in the Silver Stream Mine in Loc Modan, so hop the tram to Ironforge and then head out through the northern pass to enter the loc. The mine is halfway between the lake and the road. And nestled between

two large hills. You'll know you are getting close when you start to see kobalds. Once there you will find the gems inside abandoned crates.
Return with your items and take them to Wynee Larson in the Larson Clothing shop near the mage tower. He'll stitch your new robe together and give it to you free of charge.
If you are Horde go to the mage district in the Undercity and talk to Anistasia Hartwell. She also needs you to investigate an arcane distubance, this time from the alchemy shop. Pick up some coffers and a scroll of manifestation and head to Algernon's Alchemy shop. If you can't find it on the map just ask a guard for an alchemy trainer. At the alchmy shop use the scroll of manifestation to make the rift creatures visible and carefully pull one away. Beat it down till it's nearly dead then use the coffer of containment. Once you have collected three return back to Anastasia.
Your next task is to collect the materials necessary for your robe. To get the mana gems you need head south into Silverpine until you reach Ambermill. Kill the Dalaran mages here until you have collected six mana gems. While you are doing this collect at least ten pieces of linen cloth. When you are finished, head back to the Undercity and the mage's quarters tailoring shop. Josef Gregorian will stitch together your new robe for you free of charge.
Wand Quest
At level 38 you will get your first important mage quest. There is a lot of work involved, and it requires a trip into the scarlet monastery, but the reward you get will last you into your fifties.
To begin, head into the center of Dustwallow Marsh and find a woman named Tabetha. She will give you two different quests that ultimately lead to one final quest. First you must gather the materials to make your wand. The first item is a piece of jade, which you can buy from the AH. The second item is several bolt charged brambles which are a little more difficult to obtain. Head to the Arathi Highlands and the Witherbark troll village in the south east. Start killing the trolls to gather Witherbark Totem sticks until you have ten. After you have ten combine them into a bundle and head to the Stones of outer binding just south and east of Refuge Point. Be careful of the wind elementals nearby and head into the center. Click the stone inside and wait for your bundle to fully charge.

The second task is simpler, but takes a while longer. You need to find a book for Tabitha and the only known copy belongs to the original author. Hop a boat to Kalimdor and head to the shimmering flats in Thousand Needles. Once you are at the racing track locate a human mage named Tirth. Tirth has the book you need, but it's locked away and he forgot the password. His aprentice knows it, but he doesn't know where he is. Now, it gets weird. Look around the race track until you find a chicken. Target it and then type /beckon. This will break the assistant free from a curse and he will give you the password. Tirth will open the box, then remember that he doesn't have the book after all ><. He sold it to a member of the scarlet crusade and is now in the scarlet monastery library. In order to reach it you will need a full party of at least level 38 players. Enter the library wing of the monestary and head back towards Doan. Right before his room start to check the book cases until you find Rituals of Power. After your group has disbanded head back to Tabitha with the book and your bolt charged bramble.
Talk to Tabitha one more time and she will begin the ritual to make your wand. Try to pick the one that will match your play style. If you use mostly fire damage take the ragefire wand. But if you use mostly ice take the icefurry.
Orb Quest
After getting your wand you can move up to a new weapon. Just like the wand, Tabitha will make it for you if you manage to bring her the items she needs.
The first item is an Infernal Orb. This is a drop from Burning Blade Summoners in Desolace. The best place to find these is at the southern end of Manaroc Coven near some night elf ruins. They are found all over the coven, but the ones further north are surrounded by lots of demons.
Once you have returned with the orb you must exorcise it. Tabitha will take it out to her garden and release the demon inside. While she is doing this make sure to be far away on the dock so you have lots of distance. When the demon is summoned hit it fireballs until it gets into range. Freeze it with frost nova, blink/run away and fireball it again. By this point it should be almost dead so start to kite it with frost attacks.

Your next step is to gather a power source for your orb. This can be found inside the Uldaman instance from the Obsidian sentinel. He is rather deep inside by the back door and will often use Reflect, making your magic somewhat useless. You'll need to definitely get some help with this part, but you can easily do it during a regular Uldaman run. Once you have the power source return to Tabitha for the final step.
In order to charge your orb you need to gather mana from several mana rift beasts. Tabitha will summon them outside in her garden and you will have a set time limit of ten minuets to kill enough. While she begins the summoning ritual stand on the dock and buff yourself with dampen magic. Pull each mana surge one at a time and always keep yourself high with health and mana. Once you have killed twelve Tabitha will give you your new weapon.
Both weapons are good, but the orb is slightly better if you happen to have a main hand weapon with at least nine spell damage.
Level 52 Quest
At level 52 you will get another class specific quest. Head to northwestern Azshara to Archmage Xylem for the first step of the quest. To get to the archmage you need to teleport to his tower with the help of his assistant Sanath lim-yo. You can find him directly north of the first fork in the road. Xylem's first task is to gather some samples of glittering dust. The dust is being held by a group of blood elf surveyors to the west along the sea side cliffs. Kill as many as it takes and try to keep flame ward up since they use mostly fire attacks. After you have enough head back to Xylem for the next step.
Now Xylem wants you to bring some pieces of enchanted coral. This is held by the spitelash naga around the ruined temples. Hunt down the sirens specifically until you have six pieces before returning to Xylem. Most of the naga in this area specialize in frost attacks so try to keep frost ward up when you can. And if you have a hard time finding some be sure to check inside the temples for more.

The final step is to retrieve an arcane shard that Xylem lost long ago. Unfortunately it is in the stomach of a dragon. Gather a full group of level fifty and up players and head to the sunken temple in the swamp of sorrows. The dragon Morphaz is in the lowest part of the temple, but before you reach him you must fight through a host of trolls and kill six channelers that have locked off the lowest level. Inside the lowest

level and off in one of the side rooms Morphaz and his friend Hazza will be flapping around. The fight is pretty simple and once you have defeated him return with the shard to get your reward.
In my personal opinion the necklace is the best of the three. It will last you until you head to Outlands and the only good necklaces prior to this are found deep inside unpopular dungeons. The dagger is another good choice, but only if you are a frost mage. Otherwise the lack of solid stats makes it weak. The trinket is rather weak in my opinion and is more suited to burst damage. This is the first real trinket you can gain at this level and it is handy in PVP, but when grinding up to sixty it won't have many uses.
Polymorph Quest
There is one final quest for you to complete as a mage. Archmage Xylem has conducted new research and has a new version of polymorph for you to try out.
To start, Xylem will ask you to bring him a prismatic shell that he discovered recently. This shells is currently being held by Warlord Krelian inside the temple of Zin-Malor. Krelian is a male naga and be found either on the first floor near the pool, or the second floor near the entrance. Return to Xylem once you have the shell for the next step.
Now that he has the shell, Xylem wants you to test out his new spell. Head back to the temple area and use your polymorph spell on as many spitelash naga as you can. Once they have been polymorhped, they will break apart into clones. Kill the clones quickly because they won't last long, but they are very weak and can be brought down with AOE attacks. Once you have killed fifty return to Xylem for your new polymorph spell. It isn't any different from your regular polymorph, but instead of a sheep the target turns into a cute little piggy!