I use these free teleports all the time to get my 80 somewhere fast. The simple trick is in keeping these quests in your log and not handing them in. That's all you have to do to enjoy free travels to various cities and locations.
Fate, Up Against Your Will
This quest or the follow-up will provide you with a free teleport from Stormwind to a phased version of Orgrimmar which is helpful if you wanna fish up Old Crafty, get RFC achievement or just a quick way into the Durotar area. There will also remain a portal back into Stormwind inside Thrall's room.
Location: Stormwind to Orgrimmar
The Killing Time
This quest requires the previous 2 completed and is the 4th in the quest chain. It will provide a portal into a phased Undercity. I prefer the Orgrimmar portal myself though as I find it more useful.
Location: Anywhere to Undercity
Where in the World is Hemet Nesingwary?
This quest starts at Krasus Landing in Dalaran and will teleport u in a few seconds to the very center of Sholazar Basin. I really don't think it's worth handing in this quest as its been saving me a lot of time going on my herbalist/miner for a quick area sweep. Besides, the rewards are peanuts anyways.
Location: Dalaran to Sholazar Basin
Preparations for War
This quest also starts at Krasus Landing in Dalaran and will teleport u in a few seconds to your factions zep in Icecrown. Helpful if you wanna go straight to doing the dailies on the ship instead of looking for the zep on the map etc.
Location: Dalaran to Icecrown
The Keeper's Favor
This quest grants you a teleport into Moonglade from Crusaders' Pinnacle in Icecrown which could be useful for.. grinding Timbermaw rep.. grinding the nearby oozeling.. grinding the Winterspring Frostsaber quest.. or even getting your Leatherworking skill up on the little critters there.
Location: Icecrown to Moonglade
The Boon of A'dal
This is the end of a long chain quest with some decent rewards for a starting character, but if you don't turn this quest in then it is essentially treated like a portal to Dalaran from Shattrath. Not very useful for most, but people doing, say, Old Man Barlo's fishing may want to simply not turn it in. Each time you pick up the quest you are ported to Dalaran.
Location: Shattrath to Dalaran
Fate, Up Against Your Will
This quest or the follow-up will provide you with a free teleport from Stormwind to a phased version of Orgrimmar which is helpful if you wanna fish up Old Crafty, get RFC achievement or just a quick way into the Durotar area. There will also remain a portal back into Stormwind inside Thrall's room.
Location: Stormwind to Orgrimmar
The Killing Time
This quest requires the previous 2 completed and is the 4th in the quest chain. It will provide a portal into a phased Undercity. I prefer the Orgrimmar portal myself though as I find it more useful.
Location: Anywhere to Undercity
Where in the World is Hemet Nesingwary?
This quest starts at Krasus Landing in Dalaran and will teleport u in a few seconds to the very center of Sholazar Basin. I really don't think it's worth handing in this quest as its been saving me a lot of time going on my herbalist/miner for a quick area sweep. Besides, the rewards are peanuts anyways.
Location: Dalaran to Sholazar Basin
Preparations for War
This quest also starts at Krasus Landing in Dalaran and will teleport u in a few seconds to your factions zep in Icecrown. Helpful if you wanna go straight to doing the dailies on the ship instead of looking for the zep on the map etc.
Location: Dalaran to Icecrown
The Keeper's Favor
This quest grants you a teleport into Moonglade from Crusaders' Pinnacle in Icecrown which could be useful for.. grinding Timbermaw rep.. grinding the nearby oozeling.. grinding the Winterspring Frostsaber quest.. or even getting your Leatherworking skill up on the little critters there.
Location: Icecrown to Moonglade
The Boon of A'dal
This is the end of a long chain quest with some decent rewards for a starting character, but if you don't turn this quest in then it is essentially treated like a portal to Dalaran from Shattrath. Not very useful for most, but people doing, say, Old Man Barlo's fishing may want to simply not turn it in. Each time you pick up the quest you are ported to Dalaran.
Location: Shattrath to Dalaran