Most large cities have a fixed portal to somewhere, usually located in the part of town where mages congregate. Portals to another major city will work for anyone, but portals which take you to a combat zone will function only if you are powerful enough to join that particular battle.
In the entrance to the Mages' Tower in the Mage Quarter there is a portal that will take you to the battle front where Alliance forces are fending off an incursion by the Iron Horde.
Climbing up to the Mages' Sanctum, you will find a portal to Outland. It takes you to the Stair of Destiny in the Hellfire Peninsula.
In the War Room in Stormwind Keep, there is a portal to Stormshield, Ashran for those who have established a garrison in Draenor.
The Eastern Earthshrine is located in the outskirts of Stormwind, below the keep. There are several portals there that can take you to Vashj'ir, Deepholm, the Twilight Highlands, Tol Barad, Mount Hyjal and Uldum. These portals will open for you once you have completed appropriate quests that become available when you are ready to face challenges in these places. There is a small gate behind the Hero's Call Board in the Dwarven District. Go out, down the stairs to your right and up the hill. The Earthshrine is in the middle of the small lake. You will also find the Pandaren here. They keep a portal open to Paw'don Village in Pandaria.
In the Mystic Ward, in the Mages' building, a portal takes you to the Stair of Destiny in Outland's Hellfire Peninsula.
Near the mage trainers in the Exodar, and in the Temple of the Moon in Darnassus are two portals. One set takes you between these two cities; the other one goes the the Hellfire Peninsula in Outland.