Here is an extensive list of dungeons (or instances) that you can find in World of Warcraft, as well as those that were added with The Burning Crusade and The Wrath of the Lich King expansions.
Number in brackets represents the minimum level required to enter the instance, followed by the suggested level (full group) and then the instance name followed by its name as used in chat.
World of Warcraft
(8) 13-16 Ragefire Chasm (RFC)
(10) 17-20 The Deadmines (Dm, VC)
(10) 17-20 Wailing Caverns (WC)
(10) 18-21 Shadowfang Keep (SFK)
(10) 22-24 Blackfathom Deeps (BFD)
(15) 24-29 The Stockades (Stocks)
(15) 24-27 Razorfen Kraul (RFK)
(15) 25-28 Gnomeregan (Gnomer)
(20) 30-32 Scarlet Monastery: Graveyard (SM GY)
(20) 33-35 Scarlet Monastery: Library (SM Lib)
(25) 34-37 Razorfen Downs (RFD)
(20) 35-37 Scarlet Monastery: Armory (SM Arm)
(20) 36-40 Scarlet Monastery: Cathedral (SM Cath)
(30) 36-40 Uldaman (Ulda)
(35) 43-46 Zul'Farrak (ZF)
(35) 42-48 Maraudon (Mara)
(35) 47-50 Temple of Atal'Hakkar (Sunken Temple, ST)
(40) 48-56 Blackrock Depths (BRD)
(45) 55-58 Dire Maul: East (DM East)
(45) 54-60 Lower Blackrock Spire (LBRS)
(45) 57-60 Dire Maul: West (DM West)
(45) 57-60 Dire Maul: North (DM North)
(45) 58-60 Stratholme (Strat)
(45) 58-60 Scholomance (Scholo)
(45) 58-60 Upper Blackrock Spire (UBRS)
(50) 60+ Zul'Gurub (ZG)
(50) 60+ Onyxia's Lair (Ony. OL)
(50) 60+ Molten Core (MC)
(60) 60+ Blackwing Lair (BWL)
(50) 60+ Ruins of Ahn'Qiraj (RAQ, AQ20)
(50) 60+ Temple of Ahn'Qiraj (TAQ, AQ40)
(51) 60+ Naxxramas (Naxx)
The Burning Crusade
(55) 60-62 Hellfire Citadel: Hellfire Ramparts (Ramps)
(55) 61-63 Hellfire Citadel: The Blood Furnace (BF)
(55) 62-64 Coilfang Reservoir: Slave Pens (SP)
(55) 63-65 Coilfang Reservoir: The Underbog (UB)
(55) 64-66 Auchindoun: Mana-Tombs (MT)
(55) 65-67 Auchindoun: Auchenai Crypts (AC)
(66) 66-68 Caverns of Time: Escape from Durnholde Keep (Durn)
(55) 67-69 Auchindoun: Sethekk Halls (Seth, Seth Halls)
(55) 68-70 Coilfang Reservoir: The Steamvault (SV)
(55) 67-69 Auchindoun: Shadow Labyrinth (SL, Slabs)
(55) 69-70 Hellfire Citadel: Shattered Halls (SH, Shatt Halls)
(66) 70 Caverns of Time: Opening the Dark Portal (Black Morass, BM)
(68) 70 Tempest Keep: The Mechanar (Mech)
(68) 70 Tempest Keep: The Botanica (Bot)
(68) 70 Tempest Keep: The Arcatraz (Arc)
(65) 70 Magisters' Terrace (MgT, Terrace)
(60) 70+ Hellfire Citadel: Hellfire Ramparts (Heroic) (H Ramps)
(60) 70+ Hellfire Citadel: The Blood Furnace (Heroic) (H BF)
(60) 70+ Hellfire Citadel: Shattered Halls (Heroic) (H BF)
(??) 70+ Coilfang Reservoir: Slave Pens (Heroic) (H SP)
(??) 70+ Coilfang Reservoir: The Underbog (Heroic) (H UB)
(??) 70+ Coilfang Reservoir: The Steamvault (Heroic) (H SV)
(??) 70+ Auchindoun: Mana-Tombs (Heroic) (H MT)
(??) 70+ Auchindoun: Auchenai Crypts (Heroic) (H AC)
(??) 70+ Auchindoun: Sethekk Halls (Heroic) (H Seth Halls)
(??) 70+ Auchindoun: Shadow Labyrinth (Heroic) (H SL, H Slabs)
(??) 70+ Caverns of Time: Escape from Durnholde Keep (Heroic) (H Durn)
(??) 70+ Caverns of Time: Opening the Dark Portal (Heroic) (H BM)
(??) 70+ Tempest Keep: The Mechanar (Heroic) (H Mech)
(??) 70+ Tempest Keep: The Botanica (Heroic) (H Bot)
(??) 70+ Tempest Keep: The Arcatraz (Heroic) (H Arc)
(??) 70+ Magisters' Terrace (Heroic) (H MgT)
(68) 70+ Karazhan (Kara)
(65) 70+ Gruul's Lair
(65) 70+ Hellfire Citadel: Magtheridon's Lair
(68) 70+ Zul'Aman
(??) 70+ Coilfang Reservoir: Serpentshrine Cavern
(??) 70+ Tempest Keep: The Eye
(65) 70+ Caverns of Time: Battle for Mount Hyjal
(70) 70+ Black Temple
(70) 70+ Sunwell Plateau
Wrath of the Lich King
(65) 70-72 Utgarde Keep
(66) 71-73 The Nexus
(67) 72-74 Azjol-Nerub
(68) 73-75 Ahn'kahet: The Old Kingdom
(69) 74-76 Drak'Tharon Keep
(70) 75-77 The Violet Hold
(71) 76-78 Gundrak
(72) 77-79 Halls of Stone
(75) 80 Halls of Lightning
(75) 80 The Oculus
(75) 80 Caverns of Time: Culling of Stratholme
(75) 80 Utgarde Pinnacle
(80) 80+ Utgarde Keep (Heroic Mode)
(80) 80+ Azjol-Nerub (Heroic Mode)
(80) 80+ Drak'Tharon Keep (Heroic Mode)
(80) 80+ Halls of Stone (Heroic Mode)
(80) 80+ Halls of Lightning (Heroic Mode)
(80) 80+ The Nexus (Heroic Mode)
(80) 80+ The Oculus (Heroic Mode)
(80) 80+ Caverns of Time: Culling of Stratholme (Heroic Mode)
(80) 80+ Utgarde Pinnacle (Heroic Mode)
(80) 80+ Ahn'kahet: The Old Kingdom (Heroic Mode)
(80) 80+ The Violet Hold (Heroic Mode)
(80) 80+ Gundrak (Heroic Mode)
(77) 80+ Naxxramas
(??) 80+ Obsidian Sanctum
(??) 80+ Vault of Archavon
(??) 80+ Ulduar Raid
(??) 80+ The Eye of Eternity
(??) 80+ Icecrown Citadel
