Vanilla Legendaries: In the original game there are two legendary weapons you can still get. These include Sulfuras, Hand of Ragnaros and Thunderfury, Blessed Blade of the Windseeker. The former is made from items you can gather in Molten Core, one of the tougher instances in the original World of Warcraft. The latter is a one handed sword dropped by Thunderaan. To summon this boss, you'll need to gather a good amount of Elementium, a super rare item that only appears in Blackwing Lair. You'll also need some rare item drops out of Molten Core.
Burning Crusade Legendaries
There are two legendary items that drop in the Burning Crusade. They include the Warglaive of Azzinoth (mainhand and offhand) and Thori'dal, the Stars' Fury. The Warglaive is technically one item, but there are two versions - both of which drop from Illidan Stormrage. You can carry both blades as a dual wielder (available for Warriors, Rogues, and DKs). The second legendary is Thori'dal, a bow that drops from Kil'jaeden in the Sunwell Plateau.
Wrath Legendaries: In Wrath of the Lich King, there are two legendary weapons. The first is Val'anyr, Hammer of Ancient Kings. This is a one handed mace which can be used by Druids, Shaman, Paladins, and Priests. You will need 30 fragments of the weapon to forge it, which drop from bosses in the Ulduar raid.
The second weapon in Wrath is Shadowmourne, a two-handed ax which requires you to complete a number of quests and gather reagents only available in Icecrown Citadel. These fragments are only available in 25 player or heroic mode.
Future Legendaries: Right now the Cataclysm Legendaries have not yet been announced. That said, we know they are coming. Originally we thought Ashbringer might be available, but that seems unlikely after what happened to end Wrath's storyline.
And of course, there will eventually be new legendaries for raid instances in Cataclysm like Firelands. When that happens, be prepared for an epic grind to land all of the pieces needed to create your new legendary weapon.